Tautologies and Contradictions

JEE Main Mathematics · Mathematical Reasoning · 8 questions, latest first

• Among the two statements (S 1):(p ⇒ q) ∧(p ∧(∼ q)) is a contradiction and (S 2):(p ∧ q) ((∼ p) ∧ q) (p ∧(∼ q)) ((∼ p) ∧(∼ q)) is…202312 April, Shift 1 · Q20
• Among the statements (S1): (p ⇒ q) ((∼ p) ∧ q) is a tautology (S2): (q ⇒ p) ⇒((∼ p) ∧ q) is a contradiction20236 April, Shift 2 · Q20
• Which of the following statements is a tautology?20231 February, Shift 2 · Q80
• The number of values of r ∈{p, q, ∼ p, ∼ q} for which ((p ∧ q) ⇒(r q)) ∧((p ∧ r) ⇒ q) is a tautology, is:202331 January, Shift 2 · Q80
• (S 1)(p ⇒ q) (p ∧(∼ q)) is a tautology (S2) ((∼ p) ⇒(∼ q)) ∧((∼ p) q) is a contradiction. Then202331 January, Shift 1 · Q80
• Among the statements: (S1) ((p q) ⇒ r) ⇔(p ⇒ r) (S2) ((p q) ⇒ r) ⇔((p ⇒ r) (q ⇒ r))202330 January, Shift 1 · Q80
• Let Δ, ∇ ∈{∧, } be such that (p → q) Δ(p ∇ q) is a tautology. Then202325 January, Shift 2 · Q80
• The statement (p ∧(∼ q)) ⇒(p ⇒(∼ q)) is202325 January, Shift 1 · Q80