Name______________
Date____________
IB Math Studies
Review Logic
1. Given the propositions:
p: It flies q: it has wings
A. Write the implication p => q in words.
B. Write the converse for part A in words.
C. Write the inverse for part A in words.
D. Write the contrapositive for part A in words.
2. Consider the following propositions:
p: x is a prime number
q: x is a multiple of 7
Write the statements below in symbolic language.
A.) x is not a prime number and
x is a multiple of 7
B.) x is not a multiple of 7 or x is not
a prime number
C.) x is a multiple of 7 or x is a prime number, but not both.
3. Circle the pairs below that are logically equivalent. Use the truth table below.
A. p => q and ¬𝑞 => ¬𝑝
B. ¬(𝑝 Ʌ 𝑞) and ¬𝑝 V ¬𝑞
C. p  q and (p Ʌ q) Ʌ ¬𝑞
D. ¬𝑝 => ¬𝑞 and q => p
P
q
T
T
T
F
F
T
F
F
*4. A.) Complete the truth table below
Consider the proposition p and q
p: x is a number less than 10
q: x2 is a number less than 100
P
T
T
F
F
q
T
F
T
F
¬p
¬pvq
B.) Write in words the compound proposition ¬ p v q
C.) Using part (a), determine whether ¬ p v q is true or false for the case where x is a number
less than 10 and x2 is a number greater than 100
D.) Write down a value of ax for which ¬ p v q is false.
5. Consider the propositions:
p: I love swimming
Write the statements below in words.
A. p => ¬q
q: I have a pool
B. ¬𝑞 V p
6. Write the argument below in symbolic language
All students like chips
Melanie likes chips.
Hence, Melanie is a student
7. Complete the truth table below to determine if the argument in number 9 is a valid
argument.
P q
T T
T F
F T
F F
8. Consider the following statements
A. Write in logical form:
If Fred is a dog he has fur. If Fred has fur he has a cold nose.
Fred is a dog. Hence, Fred has a cold nose.
B. Complete the truth table below and determine if the
argument in part B is valid.
P q
r
p=>q q => r
p=>q Ʌ q=>r Ʌ p
(p=>q Ʌ q=>r Ʌ p) =>r
T T
T
T T
F
T F
T
T F
F
F T
T
F T
F
F F
T
F F
F
Explain why the argument in A is or isn’t valid.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
9. Consider the propositions
p: x is a multiple of 4, 18 < x < 30
q: x is a factor of 24
r: x is an even number, 18 < x < 30
A.) List the truth sets for p and r.
B.) List the truth sets of
i. p Ʌ q
ii. p Ʌ r
iii. p V q
Sets and Venn Diagrams
For numbers 1-5; A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, B = {1, 2, 3, 5, 7, 9} and C = {2, 4, 5 ,6, 8 , 10}
1. Give an element x such that 𝑥 ∈ 𝐴 and 𝑥 ∈ 𝐶
2. True or False: Set B is a subset of Set A.
3. List all the element s in 𝐵 ∩ 𝐶.
4. List all the elements in B U C.
5. If A is the Universal set for the situation, give B’.
6. Give an example of any two sets that are disjoint.
7. True or False: The N and the Z are disjoint.
8. True or false: The set of even numbers
And the set of odd numbers are disjoint.
9. True or False: 𝑄 𝑖𝑠 𝑎 𝑠𝑢𝑏𝑠𝑒𝑡 𝑜𝑓 𝑍
10. True or False: N is a subset of Z
For numbers 11- 13 list all the elements in the set described.
11. 𝐴 = {𝑥| 2 < 𝑥 ≤ 5, 𝑥𝜖𝑍}
12. 𝐴 = {𝑥| 𝑥 𝜖 𝑁, 𝑥 ≤ 6}
14. Use set builder notation to describe the set of all integers between -20 and 25.
15. Label and shade the region described on a Venn diagram.
A. 𝐴 ∩ 𝐵
B. A U B
C. A’ U B
D. 𝐴 ∩ 𝐵′
E. (A U B)’
16. Represent in a Venn Diagram; U = {{𝑥|𝑥 ∈ 𝑁, 𝑥 < 10}, A = {1, 2, 3, 4} B = { 2, 4, 6, 8,}
17. Given n(U) = 21, n(G)= 10, n(H) = 9 and n(𝐺 ∩ 𝐻) = 5.Find:
A. n(in H, but not in G)=
B. n( (G U H)’)=
C. n( G U H)=
*19. 40 Students participated in a mid-year adventure trip. 21 went sailing, 18 went sky diving,
15 went white water rafting, 8 went both sailing and sky diving, 9 went both sailing and white
water rafting, 7 went both sky diving and white water rafting, and 5 did all 3. Find the number
of students that;
A. went sailing or sky diving
B. only went sky diving
C. did not do any of these
Activities
D. did exactly 2 activities.