If $(p \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false,then $p$ is

  • A
    true
  • B
    false
  • C
    May be true or false
  • D
    Data insufficient

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Similar Questions

Which of the following is the negation of the statement "For all $M > 0$,there exists $x \in S$ such that $x \geqslant M$"?

Consider the two statements:
$(S1): (p$ $\rightarrow q) \vee (\sim q$ $\rightarrow p)$ is a tautology.
$(S2): (p \wedge \sim q) \wedge (\sim p \vee q)$ is a fallacy.
Then:

The negative of the statement $\sim p \wedge (p \vee q)$ is

The proposition $(p$ $\Rightarrow \sim p) \wedge (\sim p$ $\Rightarrow p)$ is a

Which of the following sentences are statements? Give reasons for your answer.
The sum of $5$ and $7$ is greater than $10.$

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