WGU C960 – Discrete Mathematics II Objective Assessment Review Questions and Answers | 2026 Update | 100% Correct

WGU C960 – Discrete Mathematics II
Objective Assessment Review

1. What is the cardinality of the power set of a set with 5 elements?
A) 5
B) 10
C) 25
D) 32
Answer: D
Explanation: The cardinality of the power set is 2^n, where n is the number of elements
in the original set. Therefore, 2^5 = 32.

2. In a standard deck of 52 cards, how many ways are there to choose a hand of 5
cards?
A) 52! / 5!
B) 52! / (5! * 47!)
C) 52! / 47!
D) 5^52
Answer: B
Explanation: This is a combination problem where order does not matter. The number of
ways to choose 5 cards from 52 is C(52, 5) = 52! / (5! * 47!).

3. What is the coefficient of the term x^3 y^2 in the expansion of (x + y)^5?
A) 5
B) 10
C) 15
D) 20
Answer: B
Explanation: The binomial coefficient for x^(5-2) y^2 is C(5,2) = 5! / (2! * 3!) = 10.

,4. A relation R on a set A is symmetric if:
A) For all a in A, (a, a) is in R.
B) For all a, b in A, if (a, b) is in R then (b, a) is in R.
C) For all a, b, c in A, if (a, b) and (b, c) are in R, then (a, c) is in R.
D) For all a, b in A, if (a, b) and (b, a) are in R, then a = b.
Answer: B
Explanation: The definition of a symmetric relation is that if an ordered pair (a, b) exists
in R, then its reverse (b, a) must also be in R.

5. Which of the following is a tautology?
A) P ∧ ¬P
B) P ∨ ¬P
C) P → ¬P
D) P ↔ ¬P
Answer: B
Explanation: A tautology is a statement that is always true. P ∨ ¬P is the law of excluded
middle, which is always true. P ∧ ¬P is a contradiction (always false).

6. In a connected planar graph, if V = 6 and E = 10, what is the number of faces
(F)?
A) 4
B) 5
C) 6
D) 7
Answer: C
Explanation: Euler's formula for planar graphs states V - E + F = 2. Substituting the
values, 6 - 10 + F = 2, which simplifies to -4 + F = 2, so F = 6.

7. How many edges does a complete graph K_7 have?
A) 14
B) 21
C) 28

,D) 42
Answer: B
Explanation: The number of edges in a complete graph K_n is n(n-1)/2. For K_7, this is
7*6/2 = 21.

8. What is the result of the recurrence relation a_n = a_{n-1} + 2 with a_1 = 1?
A) a_n = 2n - 1
B) a_n = 2n + 1
C) a_n = n + 1
D) a_n = n - 1
Answer: A
Explanation: This is an arithmetic progression with a common difference of 2. The closed
form is a_n = a_1 + (n-1)d = 1 + (n-1)*2 = 2n - 1.

9. How many distinct permutations are there of the letters in the word
"MISSISSIPPI"?
A) 11!
B) 11! / (4! * 4! * 2!)
C) 11! / (4! * 3! * 2!)
D) 11! / (4! * 4!)
Answer: B
Explanation: The word has 11 letters, with M=1, I=4, S=4, P=2. The number of distinct
permutations is 11! / (1! * 4! * 4! * 2!) = 11! / (4! * 4! * 2!).

10. What is the base case for the recursive definition of factorial, f(n) = n * f(n-1)?
A) f(0) = 0
B) f(1) = 0
C) f(0) = 1
D) f(1) = 2
Answer: C
Explanation: The base case for factorial is f(0) = 1. This stops the recursion and defines
the product of an empty set of numbers.

, 11. In modular arithmetic, what is 7 mod 3?
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: 7 divided by 3 is 2 with a remainder of 1. Therefore, 7 mod 3 = 1.

12. Which of the following is a valid Big-O notation for the function f(n) = 5n^2 +
3n + 2?
A) O(n)
B) O(n^2)
C) O(n^3)
D) O(log n)
Answer: B
Explanation: Big-O notation describes the upper bound. The dominant term is n^2, so
the function is O(n^2). While O(n^3) is also technically true, O(n^2) is the tightest
bound.

13. What is the probability of rolling a sum of 7 with two fair six-sided dice?
A) 1/6
B) 1/12
C) 1/18
D) 1/36
Answer: A
Explanation: There are 6 combinations that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
There are 36 total outcomes. Probability = 6/36 = 1/6.

14. A graph is a tree if it is:
A) Connected and contains a cycle.
B) Connected and acyclic.
C) Disconnected and acyclic.