Professional Discrete Math Interview Questions & Answers:

1. A _______ is an ordered collection of objects.
a) Relation
b) Function
c) Set
d) Proposition

c) Set

2. The set O of odd positive integers less than 10 can be expressed by ___________ .
a) {1, 2, 3}
b) {1, 3, 5, 7, 9}
c) {1, 2, 5, 9}
d) {1, 5, 7, 9, 11}

b) {1, 3, 5, 7, 9}

3. What is Discrete Math?

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

4. What is the Cartesian product of A = {1, 2} and B = {a, b}?
a) {(1, a), (1, b), (2, a), (b, b)}
b) {(1, 1), (2, 2), (a, a), (b, b)}
c) {(1, a), (2, a), (1, b), (2, b)}
d) {(1, 1), (a, a), (2, a), (1, b)}

c) {(1, a), (2, a), (1, b), (2, b)}

5. Power set of empty set has exactly _____ subset.
a) One
b) Two
c) Zero
d) Three

a) One

6. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?
a) True
b) False

b) False
Let A = {1, 2} and B = {a, b}. The Cartesian product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not equal to A x B.

7. What is the cardinality of the set of odd positive integers less than 10?
a) 10
b) 5
c) 3
d) 20

b) 5

8. Which of the following two sets are equal?
a) A = {1, 2} and B = {1}
b) A = {1, 2} and B = {1, 2, 3}
c) A = {1, 2, 3} and B = {2, 1, 3}
d) A = {1, 2, 4} and B = {1, 2, 3}

c) A = {1, 2, 3} and B = {2, 1, 3}

9. What is the Cardinality of the Power set of the set {0, 1, 2}.
a) 8
b) 6
c) 7
d) 9

a) 8

10. The members of the set S = {x | x is the square of an integer and x < 100} is _________________.
a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

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11. A function is said to be ______________, if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f.
a) One-to-many
b) One-to-one
c) Many-to-many
d) Many-to-one

b) One-to-one

12. The set of positive integers is _________ .
a) Infinite
b) Finite
c) Subset
d) Empty

a) Infinite

13. The value of ⌊1/2.⌊5/2⌋ ⌋ is _______________.
a) 1
b) 2
c) 3
d) 0.5

a) 1

14. Which of the following function f: Z X Z → Z is not onto?
a) f(a, b) = a + b
b) f(a, b) = a
c) f(a, b) = |b|
d) f(a, b) = a - b

c) f(a, b) = |b|

15. The domain of the function that assign to each pair of integers the maximum of these two integers is ________.
a) N
b) Z
c) Z +
d) Z+ X Z+

d) Z+ X Z+

16. Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ________.
a) 6x + 9
b) 6x + 7
c) 6x + 6
d) 6x + 8

a) 6x + 9

17. __________ bytes are required to encode 2000 bits of data,
a) 1
b) 2
c) 3
d) 8

b) 2

18. The inverse of function f(x) = x3 + 2 is __________.
a) f -1 (y) = (y - 2) 1/2
b) f -1 (y) = (y - 2) 1/3
c) f -1 (y) = (y) 1/3
d) f -1 (y) = (y - 2)

b) f -1 (y) = (y - 2) 1/3

19. The function f(x) = x3 is bijection from R to R. Is it True or False?
a) True
b) False

a) True

20. The g -1({0}) for the function g(x)= ⌊x⌋ is ________.
a) {x | 0 ≤ x < 1}
b) {x | 0 < x ≤ 1}
c) {x | 0 < x < 1}
d) {x | 0 ≤ x ≤ 1}

d) {x | 0 ≤ x ≤ 1}

21. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
a) True
b) False

a) True

22. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set ___________.
a) {1, 2}
b) {5, 6}
c) {2, 5}
d) {1, 6}

a) {1, 2}

23. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________.
a) {1, 2, 6, 1}
b) {1, 2, 5, 6}
c) {1, 2, 1, 2}
d) {1, 5, 6, 3}

b) {1, 2, 5, 6}

24. Which of the following two sets are disjoint?
a) {1, 3, 5} and {1, 3, 6}
b) {1, 2, 3} and {1, 2, 3}
c) {1, 3, 5} and {2, 3, 4}
d) {1, 3, 5} and {2, 4, 6}

d) {1, 3, 5} and {2, 4, 6}

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25. Two sets are called disjoint if there _____________ is the empty set.
a) Union
b) Difference
c) Intersection
d) Complement

c) Intersection