MGF1131 MATH IN CONTEXT
COMPREHENSIVE MASTERY
QUESTIONS AND ANSWERS
1. Which of the following is the symbolic negation of the statement ‘Some birds cannot fly’?
A. All birds can fly.
B. No birds can fly.
C. Some birds can fly.
D. All birds cannot fly.
Answer: A
Conceptual Explanation: The negation of ‘Some are not’ is ‘All are’. Therefore, the
negation of ‘Some birds cannot fly’ is ‘All birds can fly’.
2. In a Venn diagram with three overlapping sets A, B, and C, how many distinct regions are
created including the region outside all sets?
A. 6
B. 8
C. 7
,D. 9
Answer: B
Conceptual Explanation: Three overlapping sets create 2^3 = 8 regions: one for each set
alone (3), intersections of two (3), intersection of all three (1), and the exterior region (1).
3. A logical argument is considered ‘valid’ if:
A. It is impossible for the premises to be true and the conclusion false simultaneously.
B. The premises are all true.
C. The conclusion is true regardless of the premises.
D. The conclusion follows from the premises only when the premises are false.
Answer: A
Conceptual Explanation: Validity refers to the structure of the argument; if the truth of
the premises necessitates the truth of the conclusion, the argument is valid.
4. Find the number of subsets for a set containing 7 elements.
A. 49
B. 127
C. 128
D. 64
Answer: C
, Conceptual Explanation: The number of subsets for a set with n elements is 2n. 27 = 128.
5. Which logical fallacy occurs when the conclusion is assumed in one of the premises?
A. Ad Hominem
B. False Dilemma
C. Straw Man
D. Circular Reasoning
Answer: D
Conceptual Explanation: Circular reasoning (begging the question) occurs when the
reasoner begins with what they are trying to end with.
6. If the odds in favor of an event are 3 to 5, what is the probability that the event will occur?
A. 0.6
B. 0.375
C. 0.625
D. 0.3
Answer: B
Conceptual Explanation: Probability = Favorable / (Favorable + Unfavorable). Here, 3 / (3
+ 5) = 3/8 = 0.375.
COMPREHENSIVE MASTERY
QUESTIONS AND ANSWERS
1. Which of the following is the symbolic negation of the statement ‘Some birds cannot fly’?
A. All birds can fly.
B. No birds can fly.
C. Some birds can fly.
D. All birds cannot fly.
Answer: A
Conceptual Explanation: The negation of ‘Some are not’ is ‘All are’. Therefore, the
negation of ‘Some birds cannot fly’ is ‘All birds can fly’.
2. In a Venn diagram with three overlapping sets A, B, and C, how many distinct regions are
created including the region outside all sets?
A. 6
B. 8
C. 7
,D. 9
Answer: B
Conceptual Explanation: Three overlapping sets create 2^3 = 8 regions: one for each set
alone (3), intersections of two (3), intersection of all three (1), and the exterior region (1).
3. A logical argument is considered ‘valid’ if:
A. It is impossible for the premises to be true and the conclusion false simultaneously.
B. The premises are all true.
C. The conclusion is true regardless of the premises.
D. The conclusion follows from the premises only when the premises are false.
Answer: A
Conceptual Explanation: Validity refers to the structure of the argument; if the truth of
the premises necessitates the truth of the conclusion, the argument is valid.
4. Find the number of subsets for a set containing 7 elements.
A. 49
B. 127
C. 128
D. 64
Answer: C
, Conceptual Explanation: The number of subsets for a set with n elements is 2n. 27 = 128.
5. Which logical fallacy occurs when the conclusion is assumed in one of the premises?
A. Ad Hominem
B. False Dilemma
C. Straw Man
D. Circular Reasoning
Answer: D
Conceptual Explanation: Circular reasoning (begging the question) occurs when the
reasoner begins with what they are trying to end with.
6. If the odds in favor of an event are 3 to 5, what is the probability that the event will occur?
A. 0.6
B. 0.375
C. 0.625
D. 0.3
Answer: B
Conceptual Explanation: Probability = Favorable / (Favorable + Unfavorable). Here, 3 / (3
+ 5) = 3/8 = 0.375.
