Mathematics Practice Test – Logical Reasoning

Consider the statement:

P: Aristotle is a man
Q: All men are mortal
R: Aristotle is mortal

Which of the following statement is true? (WASSCE 2017)

A. P ∨ Q ⇒ R
B. P ⇒ Q ∨ R
C. P ⇒ Q ∧ R
D. P ∧ Q ⇒ R

Let

p: All state capitals are big cities
q: Benin is a state capital

Which of the following statements is true? (NECO 2018)

A. All big cities are state capitals
B. All state capitals are not big cities
C. Benin is a big city
D. Benin is not a state capital

Which of the following implication has the same truth value as p ⇒ q?

A. ∼p ⇒ q
B. p ⇒ q∼
C. ∼p ⇒ ∼q
D. ∼q ⇒ ∼p

The implication x  y is equivalent to_____ (WASSCE 2020 FM)

A. x ⇒ y
B. ∼x ⇒ y
C. ∼x ⇒ ∼y
D. ∼y ⇒ ∼x

Let

p: I pass mathematics
q: I pass physics

Conclusion:
I pass mathematics if and only if I pass physics. Translate the conclusion into symbol. (NECO 2022)

A. p ⇒ q
B. p ⇐ q
C. p ⇔ q
D. p ⇔  ∼q