Test: Mathematical Logic- 2 - Computer Science Engineering (CSE) MCQ

“If X then Y unless Z” is represented by which of the following formulas in propostional logic? ("_") is negation, “∧” is conjunction, and "→" is implication)

Let P, Q and, R be three atomic propositional assertions. Let X denote ( P v Q ) → R and Y denote (P → R) v (Q → R). Which one of the following is a tautology?

Which one of the following is the most appropriate logical formula to represent the statement:
“Gold and silver ornaments are precious”
The following notations are used:
G(x): x is a gold ornament
S(x): x is a silver ornament
P(x): x is precious

Suppose the predicate P(x, y, t) is used to represent the statement that person x can fool person y at time t. Which one of the statements below expresses best the meaning of the formula​

What is the logical translation of the following statements?
“None of my friends are perfect"

Consider the statement:
"Not all that glitters is gold"
Predicate glitters (x) is true if x glitters and predicate gold (x) is true if x is gold. Which one of the following logical formulae represents the above statement?

Which one of the following propositional logic formulas is TRUE when exactly two of p, q, and r are TRUE?

Consider the following statements:
P : Good mobile phones are not cheap
Q : Cheap mobile phones are not good
L : P implies Q
M : Q implies P
N : P is equivalent to Q
Which one of the following about L, M and N is CORRECT?

Which one of the following Boolean expressions is NOT a tautology?

Consider the following two statements:
S₁: If a candidate is known to be corrupt, then he will not be elected.
S₂: If a candidate is kind, he will be elected. 
Which one of the following statements follows from S₁ and S₂ as per sound inference rules of logic?