Exercises. Sec 3.3: Conditional and Biconditional
For a conditional p → q:
statement p is called the _______________ and
statement q is called the _______________.
If p is true, q is false, find the truth value of ~(p ᴧ q) → ~p
Construct a truth table for (p ᴠ r) ↔ (p ᴧ q)
p
T
T
T
T
F
F
F
F
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
(p ᴠ r)
(p ᴧ q)
(p ᴠ r) ↔ (p ᴧ q)
Write the contrapositive for the statement
“If you clean up your mess, then you can play with toys.”
Find the converse of the statement v → ~u
For the following statement:
“If the ball does not bounce, then the ball is orange.”
Find the:
I. Converse
________
II. Inverse
________
III. Contrapositive ________
a. If the ball does not bounce, then the ball is orange.
b. If the ball is orange, then the ball doesn’t bounce.
c. If the ball bounces, then the ball is not orange.
d. If the ball is not orange, then the ball bounces.
e. The ball bounces or the ball is orange
Are the following statements equivalent?
(It is helpful to write each in symbolic form.)
If you activate your phone, then you get free minutes.
If you do not get free minutes, then you do not activate
your phone.
Are the following statements equivalent?
(It is helpful to write each in symbolic form.)
If you are hungry, then you will eat.
If you eat, then you are hungry.
Rewrite the following statement using the ‘if..then’
connective.
You can afford it if you read it in the newspaper.
The graph to the right
shows the results of a
poll regarding who
people think is the
greatest politician of
all time. Use the graph
to determine is the
statement below is
true or false.
Statement: If more than half of those surveyed chose
Brown or Kealty, then more than 15% chose Fowler.
The correct answer is:
A. The statement is true because the hypothesis was false
and the conclusion was true.
B. The statement is false because the hypothesis was true
and the conclusion was false.
C. The statement is false because the hypothesis was false.
D. The statement is true because the conclusion is true.