BIFS:
Date:
.
Name: ___________________________
IB MATH STUDIES: UNIT TEST
/ 38 marks 
Score:
Logic (3.4 – 3.7)
Time Allowed: 1 period
SECTION A: Answer in the space provided.
1.
IB:
[(p  q)  p] v q
(a)
(b)
Complete the truth table below for the compound statement above.
p
q
T
T
T
F
F
T
F
F
p q
(p  q)  p
These propositions p and q are given are given:
[(p  q)  p] v q
p: A shape has 4 sides
q: A shape is a quadrilateral
Express in words, the statement p  q means
Working:
Answers:
(b) ..................................................................
..................................................................
(Total 4 marks)
%
2.
Two logic propositions are given
p: Cara goes to the cinema
q: Cara studies for the test
(a)
Write in words the proposition
p  q.
(b)
Given the statement s: “If Cara goes to the cinema then Cara doesn’t study for the test”.
(i)
Write s in symbolic form.
(ii)
Write in symbolic form the contrapositive of part (b)(i).
Working:
Answers:
(a) ...................................................
(b) (i)............................................
(ii)...........................................
(Total 6 marks)
3.
The truth table below shows the truth-values for the proposition
pqpq
p
q
p
q
T
T
F
F
T
F
F
F
T
T
F
F
T
pq
pq
pqpq
F
T
T
T
F
T
T
T
T
F
T
(a)
Explain the distinction between the compound propositions, p  q and p  q.
(b)
Fill in the four missing truth-values on the table.
(c)
State whether the proposition p  q   p   q is a tautology, a contradiction or
neither.
Working:
Answers:
(a) ...................................................
...................................................
...................................................
(c) ...................................................
(Total 6 marks)
4.
(a)
(i)
(ii)
Complete the truth table below.
q
T
F
F
T
F
F
T
F
T
T
F
F
F
T
T
q
T
pq
(p  q)
p
p
p  q
State whether the compound propositions (p  q) and p  q are equivalent.
(4)
Consider the following propositions.
p: Amy eats sweets
q: Amy goes swimming.
(b)
Write, in symbolic form, the following proposition.
Amy either eats sweets or goes swimming, but not both.
(2)
(c) Write the expression p   q as a logic statement.
(2)
Working:
Answers:
(a) (ii)............................................
(b) ..................................................
(c) ……………………………………
(Total 8 marks)
SECTION B: Answer on the provided IBO lined examination paper.
5.
Let p stand for the proposition “I will walk to school”. Let q stand for the proposition “the sun is
shining”.
(a)
Write the following statements in symbolic logic form
(i)
“If the sun is shining then I will walk to school.”
(ii)
“If I do not walk to school then the sun is not shining.”
(4)
(b)
Write down, in words, the inverse of the statement
“If the sun is shining then I will walk to school.”
(2)
(Total 6 marks)
6.
Consider the following logic statements:
p: x is a factor of 6
q: x is a factor of 24
(a)
Write p  q in words.
(1)
(b)
Write the converse of p  q.
(1)
(c)
State if the converse is true or false and give an example to justify your answer.
(2)
(Total 4 marks)
7.
The propositions p, and q are defined as follows:
p: the course is worth taking
q: the grading is lenient in this course
Write the following argument using p, q and logic symbols or connectives only.
Either the grading is lenient in this course, or the course is not worth taking.
But the grading is not lenient. Therefore, the course is worth taking.
(Total 4 marks)