Consider the following statements:
$r: \text{If } p \to q \text{ is false, then } p \lor q \text{ is false.}$
$s: \text{If } p \leftrightarrow q \text{ is false, then } p \lor q \text{ is false.}$
The truth values of $r \to s$ and $s \to r$ are respectively:

  • A
    $T, T$
  • B
    $T, F$
  • C
    $F, T$
  • D
    $F, F$

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Similar Questions

The correct simplified circuit diagram for the logical statement $[\{q \wedge (\sim q \vee r)\} \wedge \{\sim p \vee (p \wedge \sim r)\}] \vee (p \wedge r)$ where $p, q, r$ represent switches $S_1, S_2, S_3$ respectively.

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

The Boolean expression $\sim(p \vee q) \vee (\sim p \wedge q)$ is equivalent to:

Find the component statements of the following compound statement:
The sky is blue and the grass is green.

Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Which of the following is true regarding these statement patterns?

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