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

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

Explore More

Similar Questions

The negation of $\sim s \vee (\sim r \wedge s)$ is equivalent to

Given below are two statements:
$p: 25 \text{ is a multiple of } 5.$
$q: 25 \text{ is a multiple of } 8.$
Write the compound statements connecting these two statements with "And" and "Or". In both cases,check the validity of the compound statement.

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

If $p$ : the function $f(x) = x$ is an even function,$q$ : ${}^nC_m$ is a whole number wherever defined,and $r$ : if $\overrightarrow{c} = \overrightarrow{a} + \lambda \overrightarrow{b}$,then the vectors $\overrightarrow{a}, \overrightarrow{b}$,and $\overrightarrow{c}$ are linearly dependent. Which one of the following statements is true?

Difficult
View Solution

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo