# A level Mathematical Logic Quiz 1

#### Quiz Description

In this quiz, A level logic quiz, we will basically be talking about what logic is all about, the definition, what tautology and contradiction in mathematical logic is all about as this quiz with 15 questions has been solely set on the tautology and contradiction of mathematical statements.

Mathematical logic is the application of mathematical techniques to logic. Tautology is a situation whereby the truth values on the last column of a truth table are all true and a contradiction is the reverse of a tautology as in all the truth values in the last column of the truth table are all false.

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Which of the following propositions is tautology?

Correct
• (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

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

Which of the following is/are tautology?

Correct
• 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

Correct
• valid
• well informed formula
• non of these

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

Correct
• 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

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

Which of the following is a declarative statement?

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

P → (Q → R) is equivalent to

Correct
• (P ^ Q) → R
• (P v Q) → R
• (P v Q) → ˥R
• non of the above

Which of the following are tautologies?

Correct
• ((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?

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

Consider two well-formed formulas in propositional logic
F1 : P →˥P F2 : (P →˥P) v ( ˥P →)
Which of the following statement is correct?

Correct
• F1 is satisfiable, F2 is unsatisfiable
• F1 is unsatisfiable, F2 is satisfiable
• F1 is unsatisfiable, F2 is valid
• F1 & F2 are both satisfiable

What can we correctly say about proposition P1:
P1 : (p v ˥q) ^ (q →r) v (r v p)

Correct
• P1 is tautology
• P1 is satisfiable
• If p is true and q is false and r is false, the P1 is true
• If p as true and q is true and r is false, then P1 is true

(P v Q) ^ (P → R )^ (Q →S) is equivalent to

Correct
• S ^ R
• S → R
• S v R
• All of the above

The functionally complete set is

Correct
• { ˥, ^, v }
• {↓, ^ }
• {↑}
• Both (b) and (c)

(P v Q) ^ (P→R) ^ (Q → R) is equivalent to

Correct
• P
• Q
• R
• True=T