Name___________________________________
Math Literacy
Midterm Review
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use Venn diagrams to determine whether the following statements are equal for all sets A and B.
1) A ∪ (B ∩ C)ʹ, A ∪ (Bʹ ∪ Cʹ)
A) equal
B) not equal
1)
Answer: A
Draw the next figure in the pattern.
2)
2)
A)
B)
C)
D)
Answer: C
Determine if the argument is valid or invalid. Give a reason to justify answer.
3) If the bough breaks, then the cradle will fall.
The bough breaks. ∴ The cradle will fall.
A) Valid by the law of syllogism
B) Valid by the law of detachment
C) Invalid by fallacy of the inverse
D) Invalid by fallacy of the converse
3)
Answer: B
Solve the problem.
4) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the
committee can have at most two girls?
A) 5665 ways
B) 4620 ways
C) 5170 ways
D) 4410 ways
4)
Answer: B
5) Bob and Fred play the following game. Bob rolls a single die. If an even number results, Bob must
pay Fred the number of dollars indicated by the number rolled. On the other hand, if an odd
number is rolled, Fred must pay Bob the number of dollars indicated by the number rolled. Find
Fredʹs expectation.
A) $0
B) - $.10
C) $.25
D) $.50
5)
Answer: D
6) How many two-digit counting numbers do not contain any of the digits 1, 3, or 9?
A) 81 numbers
B) 49 numbers
C) 42 numbers
D) 72 numbers
Answer: C
1
6)
7) Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 9 shirts and 9 pairs of
pants to choose from, in how many different ways can this be done?
A) 10,584
B) 10,674
C) 10,642
D) 10,344
7)
Answer: A
8) Find the expected number of girls in a family of 7 children.
A) 3.5
B) 4
C) 3.25
8)
D) 3
Answer: A
9) A rectangle has area of 1176 square meters. Its length and width are whole numbers. Which
measurements give the smallest perimeter?
A) 6 meters by 196 meters
B) 7 meters by 168 meters
C) 28 meters by 42 meters
D) 1 meter by 1176 meters
9)
Answer: C
10) A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find
the probability that the family has at least one boy.
13
3
15
B) 1
C)
D)
A)
16
4
16
10)
Answer: A
11) How many triangles (of any size) are there in the figure?
A) 19
B) 13
C) 15
11)
D) 16
Answer: D
12) A survey of 121 college students was done to find out what elective courses they were taking. Let
A = the set of those taking art, B = the set of those taking basketweaving, and C = the set of those
taking canoeing. The study revealed the following information.
12)
n(A) = 45 n(A ∩ B) = 12
n(B) = 55
n(A ∩ C) = 15
n(C) = 40 n(B ∩ C) = 23
n(A ∩ B ∩ C) = 2
How many students were not taking any of these electives?
A) 39
B) 10
C) 31
D) 29
Answer: D
13) The odds against Chip beating his friend in a round of golf are 1 : 7. Find the probability that Chip
will beat his friend.
7
1
1
7
B)
C)
D)
A)
8
9
8
9
Answer: B
2
13)
14) A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many
ways can you get 5 apples?
A) 12 ways
B) 24 ways
C) 6 ways
D) 10 ways
14)
Answer: C
15) An employment agency required 20 secretarial candidates to type the same manuscript. The
number of errors found in each manuscript is summarized in the histogram. Find the empirical
probability that a candidate has less than four errors in the typed manuscript.
A)
1
2
B)
1
4
C)
2
5
D)
15)
1
10
Answer: C
16) A telephone call from Texas, U.S.A. to Ontario, Canada costs $ 1.75 for the first minute and $0.50
for each additional minute. How much will a 28-minute call cost?
A) $15.25
B) $28.75
C) $14.00
D) $13.50
16)
Answer: A
17) A boxer takes 3 drinks of water between each round for the first four rounds of a championship
fight. After the fourth round he starts to take his three drinks plus one additional drink between
each of the remaining rounds. If he continues to increase his drinks by 1 after each round, how
many drinks will he take between the 14th and 15th round?
A) 11 drinks
B) 10 drinks
C) 19 drinks
D) 14 drinks
17)
Answer: D
Let U = {all soda pops}, A = {all diet soda pops},
B = {all cola soda pops}, C = {all soda pops in cans},
and D = {all caffeine-free soda pops}. Describe the
set in words.
18) (A ∩ B) ∩ Cʹ
A) All non-diet, non-cola soda pops not in cans
B) All diet and all cola soda pops not in cans
C) All cola soda pops not in cans
D) All diet cola soda pops not in cans
18)
Answer: D
Use inductive reasoning to predict the next line in the pattern.
19) 9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998,001
A) 9999 x 9999 = 999,001
B) 999 x 9999 = 99,980,001
C) 9999 x 9999 = 99,980,001
D) 9999 x 9999 = 1,000,001
Answer: C
3
19)
20) 8 x 10 = 9 x 11 - 19
10 x 12 = 11 x 13 - 23
A) 12 x 14 = 13 x 15 + 25
C) 12 x 14 = 13 x 15 - 25
20)
B) 12 x 14 = 15 x 23 - 27
D) 12 x 14 = 13 x 15 - 27
Answer: D
Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ
q = ʺIʹll exercise.ʺ
21) Iʹll exercise if I donʹt eat too much.
A) ~p ∨ q
B) ~(p → q)
21)
C) ~p → q
D) ~p ∧ q
C) ~p → q
D) ~(p → q)
Answer: C
22) Iʹll exercise if I donʹt eat too much.
A) ~p ∨ q
B) ~p ∧ q
22)
Answer: C
Determine which region, I through VII, the indicated element belongs.
23) Determine in which region of the Venn diagram the letter in question would be placed.
d
A) I
B) III
C) VIII
Answer: A
4
D) V
23)
Estimate the indicated probability.
24) A dart is thrown randomly and sticks on the circular dart board shown.
R
24)
G
G
R
B
G
R
B
Assuming the dart does not land on a border between colored areas, find the probability that the
dart lands on a green area.
3
1
1
5
B)
C)
D)
A)
8
2
4
8
Answer: B
25) A survey was done at a mall in which 2000 customers were asked what type of credit card they
used most often. The results of the survey are shown in the figure below:
25)
.2%
38.9%
12.2%
32.4%
16.3%
How many of the 2000 persons surveyed use Mastercard?
A) 835
B) 775
C) 778
D) 785
Answer: C
Write the set in set-builder notation.
26) The odd natural numbers less than 57
A) {x∣x ∈ N < 56}
C) {x∣x ∈ N ≤ 55 and x is odd}
26)
B) {x∣x ∈ N ≤ 57 and x is odd}
D) {x∣x ∈ N < 57}
Answer: C
5
Express the set in roster form.
27) The set of seasons in a year
A) {winter, summer}
C) {cold, warm, hot, cool}
27)
B) {winter, spring, summer, fall}
D) {January, March, June, September}
Answer: B
Use DeMorganʹs laws if necessary.
28) If the chores are done, then we will go to the carnival and we will eat cotton candy.
Contrapositive
A) If the chores are not done, then we will not go to the carnival or we will not eat cotton candy.
B) If we go to the carnival and we eat cotton candy, then the chores are done.
C) If we do not go to the carnival or we do not eat cotton candy, then the chores are not done.
D) If we do not go to the carnival and we do not eat cotton candy, then the chores are not done.
28)
Answer: C
Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the
compound statements into symbols.
29) Jim plays football and Michael plays basketball.
29)
A) p ∨ q
B) ~p ∧ q
C) p ∨ ~q
D) p ∧ q
Answer: D
Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
30) (p → q) ∨ (q → p), (p ↔ q)
A) Equivalent
B) Not equivalent
30)
Answer: B
Translate the statement into symbols then construct a truth table.
31) p = Parker will work in an office.
q = Parker will work as a forest ranger.
r = Parker will work as a landscape architect.
Parker will not work in an office, but he will work as a forest ranger or a landscape architect.
A) p q r ~p ∧ (q ∨ r)
B) p q r ~p ∧ (q ∨ r)
T
T
T
T
F
F
F
F
C) p
T
F
F
F
T
T
F
F
q
T
F
T
F
T
F
T
F
r
T
T
T
T
F
F
F
F
T
F
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
T
F
T
T
F
T
~p ∧ (q ∨ r)
F
F
F
F
T
T
T
F
Answer: C
6
T
T
T
T
F
F
F
F
D) p
T
F
F
F
T
T
F
F
q
T
F
T
F
T
F
T
F
r
T
T
T
T
F
F
F
F
T
F
F
F
T
T
F
F
T
F
T
F
T
F
T
F
F
F
F
F
T
T
T
T
~p ∧ (q ∨ r)
T
F
F
F
T
F
F
F
31)
Solve the problem using inductive reasoning.
32) How many line segments are used in the next figure?
A) 24
B) 36
32)
C) 30
D) 27
Answer: C
SHORT ANSWER. Show all work. Algebraic solutions only. Partial Credit.
33) How many rectangles are there in the last two figures?
33)
Answer: 5 + 4 + 3 + 2 + 1 = 15 rectangles
8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 rectangles
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
34) Cʹ ∪ Aʹ
A) {w, y}
C) {s, t}
34)
B) {q, r, s, t, u, v, x, z}
D) {q, s, u, v, w, x, y, z}
Answer: B
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound
statement.
35) ~(q ∨ ~r)
35)
Answer:
True
False
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the set is well defined.
36) The set of birds nesting in trees at Elm Nature Center on March 16, 2000
A) not well defined
B) well defined
Answer: B
7
36)
Determine whether the sets are equal, equivalent, both, or neither.
37) {x | x is a real number} and
{x | x is a rational number}
A) Neither
B) Equivalent
C) Equal
37)
D) Both
Answer: A
Answer the question.
38) In order to determine premiums, life insurance companies must compute the probable date of
death. They have determined that Carl LaFong, age 34, is expected to live another 45.7 years. Does
this mean that Carl will live until he is 79.7 years old? If not, what does it mean?
A) Yes.
B) No, it means that Carl will live to be 79.7 years old, give or take a week.
C) No, it means that for a large group of persons with the same risk factors as Carl, the average
age at death would be approximately 79.7 years old.
D) No, it means that for a large group of persons with the same risk factors as Carl, at least one
person would live to an age of exactly 79.7 years old.
38)
Answer: C
Select letters to represent the simple statements and write each statement symbolically by using parentheses then
indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
39)
39) If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible
by 6.
B) p ∨ (~q → ~r); disjunction
A) (p ∧ ~q) → (~r); conditional
C) p ∧ (~q → ~r); conjunction
D) (p ∧ ~q) ↔ (~r); biconditional
Answer: A
Write the compound statement in words.
Let r = ʺThe puppy is trained,ʺ
p = ʺThe puppy behaves well,ʺ
q = ʺHis owners are happy.ʺ
40) ~r → ~q
40)
A) The puppy is not trained and his owners are not happy.
B) The puppy is trained or his owners are happy.
C) If the puppy is not trained then his owners are not happy.
D) It is not the case that if the puppy is trained then his owners are happy.
Answer: C
Use the Venn diagram to find the requested set.
41) Find Aʹ ∩ Bʹ.
9
x
41)
q
6
2
A) ∅
g
B) {6}
C) {9, 2, 6, x, q, g}
Answer: A
8
D) {9}
Find the odds.
42) The kings are separated from a deck of standard playing cards and shuffled. One is randomly
selected. What are the odds in favor of drawing a black card?
A) 1 to 2
B) 1 to 1
C) 1 to 4
D) 4 to 1
42)
Answer: B
Use truth tables to test the validity of the argument.
43) (p → q) ∧ (q → r)
43)
p ∴ r
A) Valid
B) Invalid
Answer: A
Write an equivalent sentence for the statement.
44) An number n is divisible by 3 if and only if the sum of the digits of n is divisible by 3. ( Hint: Use
the fact that (p → q) ∧ (q → q) is equivalent to p ↔ q.)
A) If a number n is divisible by 3 then the sum of the digits of n is divisible by 3, or if the sum of
the digits of n is divisible by 3 then the number n is divisible by 3.
B) The sum of the digits of n is divisible by 3 or the number n is divisible by 3.
C) A number n is divisible by 3 and the sum of the digits of n is divisible by 3.
D) If a number n is divisible by 3 then the sum of the digits of n is divisible by 3, and if the sum
of the digits of n is divisible by 3 then the number n is divisible by 3.
44)
Answer: D
Write a negation of the statement.
45) Some athletes are musicians.
A) All athletes are not musicians.
C) Some athletes are not musicians.
45)
B) All athletes are musicians.
D) No athletes are musicians.
Answer: D
Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the
compound statement. Use a reference source such as an almanac or the chart or graph provided.
46)
46)
Thirty-one percent of people watch 7 hours of TV each week or 6% do not watch 9 or more hours
of TV each week, and 18% watch 8 hours of TV each week.
A) False
B) True
Answer: B
9
Use ⊆, ⊈, ⊂, or both ⊂ and ⊆ to make a true statement.
47) {x | x ∈ N and x > 7} {x | x ∈ N and 2 < x ≤ 7}
A) ⊆ and ⊂
47)
B) ⊂
C) ⊈
D) ⊆
Answer: C
Given p is true, q is true, and r is false, find the truth value of the statement.
48) [(~p → r) ∧ (~p ∨ q)] → r
A) False
B) True
48)
Answer: A
Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is
true or false.
1
49) If is not an integer, then n is not an integer.
49)
n
1
A) If n is an integer, then is an integer. true
n
1
B) If is an integer, then n is an integer. false
n
1
C) If is an integer, then n is an integer. true
n
1
D) If n is an integer, then is an integer. false
n
Answer: D
Find the probability.
50) One digit from the number 8,969,119 is written on each of seven cards. What is the probability of
drawing a card that shows 8, 9, or 6?
8
6
5
3
B)
C)
D)
A)
7
7
7
7
50)
Answer: D
Factor the expression completely.
51) rx + sx + 5r + 5s
A) x r + s + 5
51)
B) x + 5 r + s
C) x + 5 rs
D) x - 5 r + s
B) (4z + 3)(5z - 3)
C) (20z + 3)(z - 3)
D) (4z - 3)(5z + 3)
Answer: B
52) 20z 2 + 3z - 9
A) Prime
52)
Answer: B
If the statement is true for all sets A and B, answer ʺtrue.ʺ If it is not true for all sets A and B, answer ʺfalse.ʺ Assume that
A ≠ ∅, U ≠ ∅, and A ⊂ U.
53) ∅ ⊄ ∅
53)
A) False
B) True
Answer: B
10
For the given sets, construct a Venn diagram and place the elements in the proper region.
54) Let U = {b, a, g, i, m, q, r}
A = {a, g, i, q}
B = {b, a, g, r}
54)
B)
A)
i
a
b
q
g
r
i
a
b
q
g
r
m
Answer: B
Add parentheses using the dominance of connectives and then indicate whether the statement is a negation,
conjunction, disjunction, conditional, or biconditional.
55) ~[q ∨ r → p]
55)
A) (~q ∨ r) → p; conditional
B) ~[(q ∨ r) → p]; negation
C) ~(q ∨ r) → p; conditional
D) ~[q ∨ (r → p)]; negation
Answer: B
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}.
Determine whether the statement is true or false.
56) B ⊄ B
Answer:
True
56)
False
11
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a truth table for the statement.
57) ~(p ∧ q) → ~(p ∨ q)
57)
A) p
q
~(p ∧ q) → ~(p ∨ q)
B) p
q
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
C) p
T
F
T
F
q
F
T
T
T
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
D) p
T
F
T
F
q
T
F
F
T
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
T
F
T
F
T
T
F
F
T
F
T
F
T
T
T
T
F
F
F
T
Answer: B
58) (r ∧ p) ∧ (~p ∨ t)
58)
A) r
p
t
(r ∧ p) ∧ (~p ∨ t)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
F
T
T
T
T
F
T
T
B) r
p
t
(r ∧ p) ∧ (~p ∨ t)
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
F
F
F
F
F
F
Answer: B
Use the Venn diagram shown to list the set in roster form.
59) A ∪ B ∪ C
A) {1, 5}
C) {11}
59)
B) {2, 3, 6, 7, 8, 9, 10, 14}
D) {2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14}
Answer: D
12
Identify the set as finite or infinite.
60) The set of people watching fireworks at Miller Park on July 4, 2000 at 9:45 P.M.
A) Infinite
B) Finite
60)
Answer: B
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Tell whether the statement is true or false.
61) {x | x is a counting number greater than 38}
= {38, 39, 40, ...}
Answer:
True
61)
False
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the method of writing each premise in symbols in order to arrive at a valid conclusion.
62) Hard workers sweat. Sweat brings on a chill. Anyone who doesnʹt have a cold never felt a chill.
Anyone who works doesnʹt have a cold.
A) Anyone who has a cold works hard.
B) Hard workers donʹt go to work.
C) Hard workers donʹt get colds.
D) Anyone who sweats works hard.
62)
Answer: B
Find n(A) for the set.
63) A = {x | x is a second in a minute}
A) n(A) = 12
B) n(A) = 120
63)
C) n(A) = 60
D) n(A) = Infinite
Answer: C
Show that the set is infinite by placing it in a one -to-one correspondence with a proper subset of itself. Be sure to show
the pairing of the general terms in the sets.
64) {5, 12, 19, 26, ...}
64)
B) { 5, 12, 19, 26, ..., 7n - 2, ...}
A) { 5, 12, 19, 26, ..., 7n - 12, ...}
↓ ↓ ↓ ↓ ↓
↓ ↓ ↓ ↓ ↓
{ 12, 19, 26, 33, ..., 7n - 5, ...}
{ 12, 19, 26, 33, ..., 7n + 5, ...}
C) { 5, 12, 19, 26, ..., 7n + 2, ...}
D) { 5, 12, 19, 26, ..., 7n - 2, ...}
↓ ↓ ↓ ↓ ↓
↓ ↓ ↓ ↓ ↓
{ 12, 19, 26, 33, ..., 7n + 5, ...}
{ 12, 19, 26, 33, ..., 7n + 4, ...}
Answer: B
Determine which, if any, of the three statements are equivalent.
65) I) A check was mailed to you on Friday, or the check was not mailed to you on Thursday but the
check arrived late.
II) If the check was not mailed to you on Friday, then the check was not mailed to you on
Thursday but the check arrived late.
III) The check arrived late, if and only if it was mailed to you on Friday or it was not mailed to you
on Thursday.
A) I and II are equivalent
B) I, II and III are equivalent
C) I and III are equivalent
D) None are equivalent
Answer: A
Construct a Venn diagram illustrating the following sets.
13
65)
66) Wine-Tasting Medals Consider the following chart which shows teams that won at least 8 medals
in 1999 wine-tasting competitions. Let the vineyards shown represent the universal set.
France (F)
U.S.A. (U)
Spain (S)
Italy (I)
Portugal (P)
Germany (G)
Gold Silver Bronze Total
13
10
7
30
10
5
13
31
7
4
10
21
7
5
2
14
2
7
4
13
4
2
2
8
Let A = set of teams that won at least 31 medals.
Let B = set of teams that won at least 7 gold medals.
Let C = set of teams that won at least 5 silver medals.
A)
B)
C)
D)
Answer: A
14
66)
Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound
statement.
67) One dollar has the same value as 15 dimes and one quarter has the same value as 25 pennies, or
67)
one dime has the same value as 5 nickels.
A) False
B) True
Answer: A
Determine whether the argument is valid or invalid.
68) If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of
my mother. I get sentimental. Therefore, I donʹt hear that poem.
A) Valid
B) Invalid
68)
Answer: A
Use the counting principle to obtain the answer.
69) A local department store sold carpets in 3 sizes. Each carpet came in 2 qualities. One size of carpet
came in 8 colors. The other sizes came in 2 colors. How many choices of carpet were there?
A) 24 choices
B) 32 choices
C) 12 choices
D) 36 choices
69)
Answer: A
List all subsets or determine the number of subsets as requested.
70) At MegaSalad, a salad can be ordered with some, all, or none of the following set of ingredients on
top of the salad greens: {ham, turkey, chicken, tomato, feta cheese, cheddar cheese, cucumbers,
onions, red peppers, hot peppers }. How many different variations are there for ordering a salad?
A) 512
B) 1012
C) 2048
D) 1024
70)
Answer: D
Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the set of counting
numbers and the given set. Be sure to show the pairing of the general terms in the sets.
71) {2, 4, 8, 16, ...}
A) { 1, 2,
3,
4, ..., n, ...}
B) { 1, 2,
3,
4, ...,
n, ...}
↓ ↓ ↓ ↓ ↓
↓ ↓ ↓ ↓ ↓
2
2n
{ 2, 4,
8, 16, ..., n , ...}
{ 2, 4,
8, 16, ..., 2 , ...}
C) { 1, 2,
3,
4, ..., n, ...}
D) { 1, 2,
3,
4, ..., n, ...}
↓ ↓ ↓ ↓ ↓
↓ ↓ ↓ ↓ ↓
{ 2, 4,
8, 16, ..., 2n, ...}
n
{ 2, 4,
8, 16, ..., 2 , ...}
71)
Answer: D
Solve the equation.
72) 2x 2x - 12 = -36
1
A)
3
72)
B) -0.3
C) ±3
D) 3
Answer: D
Use inductive reasoning to predict the next number in the sequence.
73) 3, 10, 17, 24, 31
A) 38
B) 34
C) 45
Answer: A
15
73)
D) 37
Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is
a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
74)
74) It is false that whales are fish and bats are birds.
A) Compound; biconditional; ↔
B) Compound; negation; ~
C) Compound; disjunction; ∨
D) Compound; conjunction; ∧
Answer: B
Evaluate the validity of the chain of conditionals.
75) Premise: If you loved me, then you would buy me a new car.
Premise: If you wanted me to be happy, then you would buy me a new car.
Conclusion: If you loved me, then you would want me to be happy.
A) Valid
B) Invalid
75)
Answer: B
Convert the compound statement into words.
76) p = ʺThe food tastes delicious.ʺ
q = ʺWe eat a lot.ʺ
r = ʺNobody has dessert.ʺ
(q ∨ p) ∧ r
A) We eat a lot and the food tastes delicious or nobody has dessert.
B) We eat a lot or the food tastes delicious or nobody has dessert.
C) We eat a lot or the food tastes delicious and nobody has dessert.
D) We do not eat a lot or the food tastes delicious and nobody has dessert.
Answer: C
16
76)