MGF1131 QUIZ 1: MATH IN CONTEXT
(HIGH DIFFICULTY) QUESTIONS AND
ANSWERS
1. Which of the following describes a set that is ‘well-defined’ in a mathematical context?
A. The collection of the best movies produced in 2024.
B. The collection of great mathematicians in the 21st century.
C. The collection of all residents in Florida who are over 6 feet tall.
D. The collection of all difficult questions on this specific exam.
Answer: C
Conceptual Explanation: A set is well-defined if it is clear whether any specific object
belongs to it. Physical height is measurable and objective, whereas ‘best’, ‘great’, and
‘difficult’ are subjective.
2. If Set A = {x | x is a prime number, 1 < x < 20} and Set B = {x | x is an odd number, 1 < x <
20}, what is the cardinality of the set (A ∩ B)?
A. 6
B. 9
,C. 8
D. 7
Answer: D
Conceptual Explanation: A = {2, 3, 5, 7, 11, 13, 17, 19}. B = {3, 5, 7, 9, 11, 13, 15, 17, 19}.
The intersection A ∩ B = {3, 5, 7, 11, 13, 17, 19}, which has 7 elements.
3. Which logical connective is represented by the symbol ‘∨’ and under what condition is the
resulting statement false?
A. Conjunction; false only if both components are false.
B. Biconditional; false if components have different truth values.
C. Conditional; false only if the first is true and the second is false.
D. Disjunction; false only if both components are false.
Answer: D
Conceptual Explanation: The symbol ∨ represents a disjunction (OR). An OR statement is
only false when both parts are false.
4. Given the statement ‘If it rains, then the ground is wet,’ which of the following represents
the contrapositive?
A. If the ground is not wet, then it did not rain.
B. If the ground is wet, then it rained.
C. If it does not rain, then the ground is not wet.
, D. It is raining and the ground is not wet.
Answer: A
Conceptual Explanation: The contrapositive of p → q is ¬q → ¬p. Thus, ‘If not wet, then
not rain’.
5. In a Venn diagram with three overlapping circles (A, B, C), which region represents A ∩ (B ∪
C)’?
A. Elements in B or C but not in A.
B. Elements in A, B, and C simultaneously.
C. Elements in A that are not in B and not in C.
D. Elements only in the intersection of B and C.
Answer: C
Conceptual Explanation: (B ∪ C)’ consists of everything outside of B and C. Intersecting
this with A leaves only the parts of A that do not touch B or C.
6. A survey of 100 students found 60 like Math, 50 like Science, and 20 like both. How many
like neither?
A. 10
B. 20
C. 30
D. 0
(HIGH DIFFICULTY) QUESTIONS AND
ANSWERS
1. Which of the following describes a set that is ‘well-defined’ in a mathematical context?
A. The collection of the best movies produced in 2024.
B. The collection of great mathematicians in the 21st century.
C. The collection of all residents in Florida who are over 6 feet tall.
D. The collection of all difficult questions on this specific exam.
Answer: C
Conceptual Explanation: A set is well-defined if it is clear whether any specific object
belongs to it. Physical height is measurable and objective, whereas ‘best’, ‘great’, and
‘difficult’ are subjective.
2. If Set A = {x | x is a prime number, 1 < x < 20} and Set B = {x | x is an odd number, 1 < x <
20}, what is the cardinality of the set (A ∩ B)?
A. 6
B. 9
,C. 8
D. 7
Answer: D
Conceptual Explanation: A = {2, 3, 5, 7, 11, 13, 17, 19}. B = {3, 5, 7, 9, 11, 13, 15, 17, 19}.
The intersection A ∩ B = {3, 5, 7, 11, 13, 17, 19}, which has 7 elements.
3. Which logical connective is represented by the symbol ‘∨’ and under what condition is the
resulting statement false?
A. Conjunction; false only if both components are false.
B. Biconditional; false if components have different truth values.
C. Conditional; false only if the first is true and the second is false.
D. Disjunction; false only if both components are false.
Answer: D
Conceptual Explanation: The symbol ∨ represents a disjunction (OR). An OR statement is
only false when both parts are false.
4. Given the statement ‘If it rains, then the ground is wet,’ which of the following represents
the contrapositive?
A. If the ground is not wet, then it did not rain.
B. If the ground is wet, then it rained.
C. If it does not rain, then the ground is not wet.
, D. It is raining and the ground is not wet.
Answer: A
Conceptual Explanation: The contrapositive of p → q is ¬q → ¬p. Thus, ‘If not wet, then
not rain’.
5. In a Venn diagram with three overlapping circles (A, B, C), which region represents A ∩ (B ∪
C)’?
A. Elements in B or C but not in A.
B. Elements in A, B, and C simultaneously.
C. Elements in A that are not in B and not in C.
D. Elements only in the intersection of B and C.
Answer: C
Conceptual Explanation: (B ∪ C)’ consists of everything outside of B and C. Intersecting
this with A leaves only the parts of A that do not touch B or C.
6. A survey of 100 students found 60 like Math, 50 like Science, and 20 like both. How many
like neither?
A. 10
B. 20
C. 30
D. 0
