Question

If $p$ and $q$ are simple propositions, then $p\Rightarrow q$ is false when.

• A. $p$ is true and $q$ is true
• B. $p$is false and $q$ is true
• C. $p$ is true and $q$ is false
• D. Both $p$ and $q$ are false

Answer 1

The correct option is C

$p$ is true and $q$ is false

Step-1: Definition of Conditional statement:

Conditional: Let $p$ and $q$be two propositions/statements then Conditional statement is defined as, if $p$ is True and $q$ is False then it gives output as False otherwise True for the remaining combinations.

It can be shown with the help of a truth table.

Notation: Conditional is denoted by the symbol $\Rightarrow$.

Step-2: Truth table for $p\Rightarrow q$

$p$	$q$	$p\Rightarrow q$
T	T	T
T	F	F
F	T	T
F	F	T

Where T is True and F is False.

From the above table, we can conclude $p\Rightarrow q$ is False if $p$is True and $q$ is False.

Hence option ‘C’ is correct.