The negation of the statement pattern $p \vee (q \rightarrow \sim r)$ is

  • A
    $\sim p \wedge (\sim q \wedge r)$
  • B
    $\sim p \wedge (\sim q \wedge \sim r)$
  • C
    $\sim p \wedge (q \wedge \sim r)$
  • D
    $\sim p \wedge (q \wedge r)$

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Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?

Among the statements:
$(S1) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow ( p$ $\Rightarrow r )$
$(S2) \quad (( p \vee q )$ $\Rightarrow r ) \Leftrightarrow (( p$ $\Rightarrow r ) \vee ( q$ $\Rightarrow r ))$

By giving a counterexample,show that the following statement is false: "If $n$ is an odd integer,then $n$ is prime."

Which of the following is false?

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