WGU C277 Finite Mathematics OA (pdf) | 2026/2027 | Objective
Assessment | Finite Mathematics
1. Which of the following is a well-defined set?
A) The collection of tall buildings in New York City
B) The set of all prime numbers less than 20
C) The group of intelligent students in a classroom
D) The collection of beautiful paintings in a museum
Correct Answer: The set of all prime numbers less than 20
Rationale: A well-defined set has clear, unambiguous criteria for
membership. Prime numbers less than 20 are precisely defined (2, 3, 5, 7,
11, 13, 17, 19). The other options rely on subjective terms like "tall,"
"intelligent," or "beautiful."
2. What is the union of sets A = {1, 2, 3, 4} and B = {3, 4, 5, 6}?
A) {1, 2, 3, 4, 5, 6}
B) {3, 4}
C) {1, 2, 5, 6}
D) {1, 2, 3, 4, 4, 5, 6}
Correct Answer: {1, 2, 3, 4, 5, 6}
Rationale: The union of two sets includes all elements present in either set,
without duplication. A ∪ B = {1, 2, 3, 4, 5, 6}. The intersection is {3, 4}, and
the symmetric difference is {1, 2, 5, 6}.
3. Which of the following describes the intersection of sets A = {x | x is a
multiple of 2} and B = {x | x is a multiple of 3}?
,A) Multiples of 5
B) Multiples of 6
C) Odd numbers
D) Prime numbers
Correct Answer: Multiples of 6
Rationale: The intersection contains numbers that are multiples of both 2 and
3, which are multiples of the least common multiple, 6.
4. If set A has 5 elements and set B has 4 elements, what is the maximum
possible size of A ∩ B?
A) 0
B) 4
C) 5
D) 9
Correct Answer: 4
Rationale: The intersection cannot exceed the size of the smaller set. Since B
has 4 elements, the maximum intersection is 4 (when B is a subset of A).
5. In a Venn diagram, the region outside all circles represents:
A) The universal set
B) The complement of the union of all sets
C) The intersection of all sets
D) The empty set
,Correct Answer: The complement of the union of all sets
Rationale: The universal set contains everything under consideration. The
area outside all circles represents elements not belonging to any of the sets
shown, which is the complement of their union.
6. A compound statement that is always true regardless of the truth values
of its components is called a:
A) Contradiction
B) Tautology
C) Contingency
D) Conjunction
Correct Answer: Tautology
Rationale: A tautology is a compound statement that is true for all possible
truth value combinations. A contradiction is always false, and a contingency
is true for some combinations and false for others.
7. The truth value of the statement "p ∧ q" is true only when:
A) p is true and q is true
B) p is true or q is true
C) p is false and q is false
D) p and q have opposite truth values
Correct Answer: p is true and q is true
, Rationale: The conjunction (p ∧ q) is true only when both component
statements are true. This is the defining characteristic of the logical AND
operator.
8. The statement "p ∨ q" is false only when:
A) p is true and q is false
B) p is false and q is true
C) p is false and q is false
D) p is true and q is true
Correct Answer: p is false and q is false
Rationale: The disjunction (p ∨ q) is false only when both component
statements are false. It is true in all other cases, reflecting the inclusive
nature of the logical OR.
9. Which of the following is logically equivalent to "If p, then q"?
A) q → p
B) ¬p ∨ q
C) ¬q → ¬p
D) p ∧ ¬q
Correct Answer: ¬p ∨ q
Rationale: The conditional statement p → q is logically equivalent to ¬p ∨ q.
This equivalence is fundamental in symbolic logic and is often used to rewrite
conditional statements.
Assessment | Finite Mathematics
1. Which of the following is a well-defined set?
A) The collection of tall buildings in New York City
B) The set of all prime numbers less than 20
C) The group of intelligent students in a classroom
D) The collection of beautiful paintings in a museum
Correct Answer: The set of all prime numbers less than 20
Rationale: A well-defined set has clear, unambiguous criteria for
membership. Prime numbers less than 20 are precisely defined (2, 3, 5, 7,
11, 13, 17, 19). The other options rely on subjective terms like "tall,"
"intelligent," or "beautiful."
2. What is the union of sets A = {1, 2, 3, 4} and B = {3, 4, 5, 6}?
A) {1, 2, 3, 4, 5, 6}
B) {3, 4}
C) {1, 2, 5, 6}
D) {1, 2, 3, 4, 4, 5, 6}
Correct Answer: {1, 2, 3, 4, 5, 6}
Rationale: The union of two sets includes all elements present in either set,
without duplication. A ∪ B = {1, 2, 3, 4, 5, 6}. The intersection is {3, 4}, and
the symmetric difference is {1, 2, 5, 6}.
3. Which of the following describes the intersection of sets A = {x | x is a
multiple of 2} and B = {x | x is a multiple of 3}?
,A) Multiples of 5
B) Multiples of 6
C) Odd numbers
D) Prime numbers
Correct Answer: Multiples of 6
Rationale: The intersection contains numbers that are multiples of both 2 and
3, which are multiples of the least common multiple, 6.
4. If set A has 5 elements and set B has 4 elements, what is the maximum
possible size of A ∩ B?
A) 0
B) 4
C) 5
D) 9
Correct Answer: 4
Rationale: The intersection cannot exceed the size of the smaller set. Since B
has 4 elements, the maximum intersection is 4 (when B is a subset of A).
5. In a Venn diagram, the region outside all circles represents:
A) The universal set
B) The complement of the union of all sets
C) The intersection of all sets
D) The empty set
,Correct Answer: The complement of the union of all sets
Rationale: The universal set contains everything under consideration. The
area outside all circles represents elements not belonging to any of the sets
shown, which is the complement of their union.
6. A compound statement that is always true regardless of the truth values
of its components is called a:
A) Contradiction
B) Tautology
C) Contingency
D) Conjunction
Correct Answer: Tautology
Rationale: A tautology is a compound statement that is true for all possible
truth value combinations. A contradiction is always false, and a contingency
is true for some combinations and false for others.
7. The truth value of the statement "p ∧ q" is true only when:
A) p is true and q is true
B) p is true or q is true
C) p is false and q is false
D) p and q have opposite truth values
Correct Answer: p is true and q is true
, Rationale: The conjunction (p ∧ q) is true only when both component
statements are true. This is the defining characteristic of the logical AND
operator.
8. The statement "p ∨ q" is false only when:
A) p is true and q is false
B) p is false and q is true
C) p is false and q is false
D) p is true and q is true
Correct Answer: p is false and q is false
Rationale: The disjunction (p ∨ q) is false only when both component
statements are false. It is true in all other cases, reflecting the inclusive
nature of the logical OR.
9. Which of the following is logically equivalent to "If p, then q"?
A) q → p
B) ¬p ∨ q
C) ¬q → ¬p
D) p ∧ ¬q
Correct Answer: ¬p ∨ q
Rationale: The conditional statement p → q is logically equivalent to ¬p ∨ q.
This equivalence is fundamental in symbolic logic and is often used to rewrite
conditional statements.
