Finite Math Week 1 Quiz – Logic & Sets

Finite Math

Week 1 Quiz – Logic & Sets

MULTIPLE CHOICE SECTION

For each section, read the instructions and choose the best answer.

1. Which of the following is a statement?

a) What is your favorite movie?

b) Study hard for this class.

c) Topeka is the capital of Kansas.

d) The Gibson SG is the coolest guitar.

2. Which of the following is a statement? a) Pepperoni is the tastiest pizza topping. b) Do you come to Milwaukee often?

c) Consider each sentence carefully.

d) Monotremes are mammals that lay eggs.

Identify the symbolic expression that best represents the following compound statements. The statement

variables are defined as follows:

p: It is Friday.

q: Bridget is going shopping.

r: It is payday.

( Versio n B )

3. If it is Friday, then Bridget is going shopping.

a) p →q

b) p ∨ q c) q → p d) p ↔ q

5. It is payday if and only if it is Friday and Bridget

is going shopping.

a) ¬p ∨ ¬q ∧ r

b) r →q

c) r ↔ ( p ∧ q)

d) p →(q ∧ r)

4. It is Friday and it is not payday.

a) p ∨ r

b) p →¬r c) p ∧ ¬r d) p ⊕ r

6. If it is not payday, then Bridget is not going

shopping. a) ¬r ↔ q b) ¬r →¬q c) ¬r ∧ ¬q d) ¬q ⊕ r

Given the following truth-­‐values for some statements p, q, and r; determine the truth-­‐value of the following statements.

p: TRUE. q: FALSE. r: TRUE.

( Finite Math Week 1 Quiz – Logic & Sets )

( Version B )

7. ¬q → r

a) True

b) False

9. p →(q ∨ r)

a) True

b) False

8. (q ∨ r) ↔ ( p ∨ q)

a) True

b) False

10. ¬( p ∧ r) ∨ q

a) True

b) False

Determine which statement is logically equivalent to the given statement.

11. ¬( p ∧ q) ≡

a) ¬p →¬q

b) ¬p ∨ ¬q

c) ¬p ∧ ¬q

d) Contradiction (F)

12. p ∨ (q ∧ r) ≡

a) ¬p →¬q

b) p ∧ r ∧ q

c) ( p ∨ q) ∧ ( p ∨ r)

d) Tautology (T)

13. (q ∧ ¬q) ≡

a) ¬p →¬q

b) q

c) ¬p ∧ ¬q

d) Contradiction (F)

Given the following set:

A = {Druid, Hunter, Mage, Paladin,Pr iest, Rogue, Shaman,Warlock,Warrior, DeathKnight}

Determine if the following set relations are true or false.

14. {Hunter, Rogue} ⊆ A

a) True

b) False

15. DeathKnight ∉ A

a) True

b) False

16.

{Pr iest, Shaman,Warlock,Warrior} ⊄ A

17. A ⊆ ∅

a) True

b) False

a) True

b) False

For the following universal set:

U = {0,1,2, 3, 4,5,6, 7,8,9,10,11,12,13,14,15}

Given the following sets:

R = {2, 3,5, 7,11,13}

S = {0,2, 4,6,8,10,12,14}

T = {1,2, 3, 4,5}

Identify the set of elements described by the following set relationships.

18. S ∪ (R ∩ T )

a) {0,1,2, 4,5,6,8,10}

b) {0,2, 3, 4,5,6,8,10,12,14}

c) {0,2, 4,6,8,10,12,14}

d) None of the Above

( c )20. (S ∪ T )

19. R \ T

a) {7,11,13} b) {3, 4,5,11} c) {0, 3, 7,13}

d) None of the Above

( c )21. S ∪ (Rc ∩ T )

a) {7,9,11,13,15}

b) {0,1, 3, 7,9,10,11,12}

c) {0,1, 3,5,6, 7,8,9,10,11,12,13,14,15}

d) None of the Above

a) ∅

b) U

c) {0,2, 3, 4,5,6, 7,8,9,10,11,12,13,14,15}

d) None of the Above

Identify the relationship depicted in the Venn Diagrams below:

22.

a) B

b) B \ A c) A ∩ B d) A \ B

23.

a) ( A ∩ B)c

b) U

c) U \ ( A ∩ B)

d) ( A ∪ B)c

24.Describe the following set using set builder notation:

A = {5,15,25, 35, 45,55,65}

a) A = {x | 5 ≤ x ≤ 65}

b) A = {x + 5 | 0 ≤ x ≤ 60} c) A = {10 x + 5 | 0 ≤ x ≤ 6} d) A = {5 x |1 ≤ x ≤ 13}

25. List the power set P(S) for the set S = {A, B,C, D, F}

a) P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},

{A, B,C},{A, B, D},{A, B, F},{A,C, D},{A,C, F},{A, D, F},{B,C, D},{B,C, F},{B, D, F},{C, D, F},

{A, B,C, D},{A, B,C, F},{A,C, D, F},{A, B, D, F}{B,C, D, F},{A, B,C, D, F}}

b) P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},

{A, B,C},{A, B, D},{A, B, F},{A,C, D},{A,C, F},{A, D, F},{B,C, D},{B,C, F},{B, D, F},{C, D, F},

{A, B,C, D, F}}

c) P(S) = {∅,{A},{B},{C},{D},{F},{A, B,C, D, F}}

d) P(S) = {∅,{A},{B},{C},{D},{F},{A, B},{A,C},{A, D},{A, F},{B,C},{B, D},{B, F},{C, D},{C, F},{D, F},

{B, A},{C, A},{D, A},{F, A},{C, B},{D, B},{F, B},{D,C},{F,C},{F, D},{A, B,C},{C, B, A},{B, A,C},

{C, D, F},{F, D,C},{A, B,C, D, F}}