Reviewer

Question 1

Consider the following sets X, Y, Z below. Which one of the following is true?
X = multiples of 3, Y = multiples of 6, Z = multiples of 9

Answer 1

Z ⊂ Y

Question 2

2. A is the set of factors of 12. Which one of the following is not a member of A?

Answer 2

5

Question 3

How many subsets does the set A = {a, b, c, d} have?

Answer 3

16
(2⁴ = 16)

Question 4

4. Which one of the following sets is infinite?

Answer 4

The set of integers less than 10
(This includes negative integers, making it infinite)

Question 5

Given sets A, B, and C, where A ⊆ B and B ⊆ C. Which statement must always be true?

Answer 5

Correct Answer: d. A is a subset of C

Question 6

6. Which of the following statements is True for a function?.

Answer 6

A function has only one output for each input

Question 7

7. Which of the following relations on the set {1, 2, 3} is transitive?

Answer 7

{(1, 2), (2, 3), (1, 3)}

Question 8

8. Which of the following relations on the set {1, 2, 3} is antisymmetric?

Answer 8

c. {(1, 1), (2, 2), (3, 3), (1, 2)}

Question 9

9. Which of the following sets of ordered pairs represents a function?

Answer 9

{(1, 2), (2, 3), (3, 4), (4, 5)}

Question 10

10. Which of the following relations on the set {1, 2, 3} is irreflexive?

Answer 10

{(1, 2), (2, 3), (3, 1)}

Question 11

11. For two matrices A and B, is matrix multiplication generally commutative?

Answer 11

No, generally AB ≠ BA

Question 12

The transpose is undefined for non-square matrices. (Statement evaluation)?

Answer 12

False (transpose is defined for any matrix, not just square ones)

Question 13

In linear algebra, what is a scalar?

Answer 13

c. A single numerical value

Question 14

Which of the following describes a zero matrix (O)?

Answer 14

A matrix where all entries are zero.

Question 15

Let A be a 3x2 matrix and B be a 2x4 matrix. What are the dimensions of A·B?

Answer 15

3 x 4

Question 16

According to the Identity Law, what is A + 0?

Answer 16

A

Question 17

What is the output of X ^ (~X ∨ Y) if X = 1 and Y = 0?

Answer 17

Correct Answer: b. 0

(X = 1, ~X = 0 → 0 ∨ 0 = 0; then 1 ^ 0 = 0)

Question 18

Which Boolean expression is equivalent to A⋅(A + B)?

Answer 18

Correct Answer: b. A
(Absorption Law)

Question 19

Which expression is equivalent to ~(A ^ B) according to De Morgan’s Laws?

Answer 19

~A ∨ ~B

Question 20

Which Boolean operation is ∧ and outputs 1 only if all inputs are 1?

Answer 20

AND (Conjunction)

Question 21

If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?

Answer 21

{3}

Question 22

What does the shaded region outside all circles in a Venn diagram represent?

Answer 22

Elements not belonging to any of the given sets

Question 23

In a three-set Venn diagram (A, B, C), what region represents elements in all sets?

Answer 23

The area where all three circles overlap

Question 24

What does the overlapping region of two circles represent?

Answer 24

Elements common to both sets

Question 25

In a Venn diagram, how is A ∪ B represented?

Answer 25

The entire area covered by circles A and B