Propositional Logic

Which of the following propositions is tautology?

• (p v q)→q
• p v (q→p)
• p v (p→q)
• Both (b) & (c)

 Which of the proposition is p^ (~ p v q) is

• A tautulogy
• A contradiction
• Logically equivalent to p ^ q
• All of above

Which of the following is/are tautology?

• a v b → b ^ c
• a ^ b → b v c
• a v b → (b → c)
• None of these

Logical expression ( A^ B) → ( C' ^ A) → ( A ≡ 1) is

• Contradiction
• Valid
• Well-formed formula
• None of these

 Identify the valid conclusion from the premises Pv Q, Q → R, P → M, ˥M

• P ^ (R v R)
• P ^ (P ^ R)
• R ^ (P v Q)
• Q ^ (P v R)

Let a, b, c, d be propositions. Assume that the equivalence a ↔ (b v ˥b) and b ↔ c hold. Then truth value of the formula ( a ^ b) → ((a ^ c) v d) is always

• true
• false
• Same as the truth value of a
• Same as the truth value of b

Which of the following is a declarative statement?

• It's right
• He says
• Two may not be an even integer
• I love you

 P → (Q → R) is equivalent to

• (P ^ Q) → R
• (P v Q) → R
• (P v Q) → ˥R
• None of these

Which of the following are tautologies?

• ((P v Q) ^ Q) ↔ Q
• ((P v Q) ^ ˥P) → Q
• ((P v Q) ^ P) → P
• Both (a) & (b)

If F1, F2 and F3 are propositional formulae such that F1 ^ F2 → F3 and F1 ^ F2→F3 are both tautologies, then which of the following is TRUE?

• Both F1 and F2 are tautologies
• The conjuction F1 ^ F2 is not satisfiable
• Neither is tautologies
• None of these