HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Verify whether the following compound propositions are tautologies or contradictions or contingency.

((p → q) ∧ (q → r)) → (p → r)

Show that (p ∧ q) ≡ ¬p v ¬q

Show that ¬(p → q) ≡ p ∧¬q

Prove that q → p ≡ ¬p → ¬q

Show that p → q and q → p are not equivalent

Show that ¬(p ↔ q) ≡ p ↔ ¬q

Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table

Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent

Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table

Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table

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The operation * defined by a * b = `"ab"/7` is not a binary operation on

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Which one of the following statements has the truth value T?

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Which one of the following statements has truth value F?

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If a compound statement involves 3 simple statements, then the number of rows in the truth table is

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Which one is the inverse of the statement (p v q) → (p ∧ q)?

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Which one is the contrapositive of the statement (p v q) → r?

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The truth table for (p ∧ q) v ¬q is given below

Which one of the following is true?

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In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is

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Which one of the following is incorrect? For any two propositions p and q, we have

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Which one of the following is correct for the truth value of (p ∧ q) → ¬p