Which Venn diagram represent the truth of the statement“All students are hard working.”

Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.

  • A
    530-a34
  • B
    530-b34
  • C
    530-c34
  • D

    None of these

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The false statement in the following is

The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

  • [JEE MAIN 2022]

Statement $\left( {p \wedge q} \right) \to \left( {p \vee q} \right)$ is