Mathematics · 2021
JEE Main · 4 August 2021, Shift 1 · Q80
If r ∈{p, q, ∼ p, ∼ q} such that the Boolean expression (∼(p q)) (p ∧ r) is equivalent to r, then r is equal to
If $\displaystyle r \in\{p, q, \sim p, \sim q\}$ such that the Boolean expression $\displaystyle (\sim(p \vee q)) \vee(p \wedge r)$ is equivalent to $\displaystyle r$, then $\displaystyle r$ is equal to
Official answer
(4)
$\displaystyle \sim q$
More from Mathematical Reasoning
- The statement ∼[p (∼(p ∧ q))] is equivalent to2023
- Which of the following is a tautology?2020
- Which of the following statements is a tautology?2023
- Let Δ, ∇ ∈{∧, } be such that (p → q) Δ(p ∇ q) is a tautology. Then2023
- (p ∧ r) ⇔(p ∧(∼ q)) is equivalent to (∼ p) when r is2022
- Contrapositive of the statement: 'If a function f is differentiable at a, then it is also continuous at a', is:2020
- For the statements p and q, consider the following compound statements: (∼ q ∧(p → q)) → ∼ p ((p q) ∧ ∼ p) → q Then which of the following statements…2021
- If p, q and r are three propositions, then which of the following combination of truth values of p, q and r makes the logical expression {(p q) ∧((∼…2023
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.