MGF1131 MATH IN CONTEXT COMPREHENSIVE QUIZ 1 QUESTIONS AND ANSWERS

MGF1131 MATH IN CONTEXT
COMPREHENSIVE QUIZ 1 QUESTIONS
AND ANSWERS




1. Which of the following is the symbolic representation of the statement: ‘It is not the case

that if it rains, the grass is wet’?

A. ~(p → q)


B. ~p → q


C. p ∧ ~q


D. ~p ∧ q


Answer: A


Conceptual Explanation: The phrase ‘It is not the case that’ negates the entire conditional

statement that follows.


2. Given the set A = {2, 4, 6, 8}, how many proper subsets does it have?

A. 16


B. 8


C. 14

,D. 15


Answer: D


Conceptual Explanation: The number of subsets is 2^n. For 4 elements, it is 2^4 = 16.

Proper subsets exclude the set itself, so 16 - 1 = 15.


3. What is the negation of the statement: ‘Some dogs are not friendly’?

A. At least one dog is friendly.


B. No dogs are friendly.


C. Some dogs are friendly.


D. All dogs are friendly.


Answer: D


Conceptual Explanation: The negation of ‘Some are not’ is ‘All are’.


4. In logic, what is the truth value of the conditional statement ‘If 5 + 5 = 11, then 2 + 2 = 4’?

A. Indeterminate


B. False


C. Invalid


D. True


Answer: D

, Conceptual Explanation: A conditional p → q is only false if the antecedent p is true and

the consequent q is false. Since 5+5=11 is false, the conditional is true regardless of the

truth value of q.


5. If n(A) = 10, n(B) = 15, and n(A ∩ B) = 4, what is n(A ∪ B)?

A. 21


B. 25


C. 19


D. 11


Answer: A


Conceptual Explanation: Using the inclusion-exclusion principle: n(A ∪ B) = n(A) + n(B) -

n(A ∩ B) = 10 + 15 - 4 = 21.


6. Which logical connector is represented by the symbol ‘∧’?

A. Disjunction (or)


B. Negation (not)


C. Conjunction (and)


D. Conditional (if…then)


Answer: C


Conceptual Explanation: The symbol ∧ represents ‘and’, which is a conjunction.