Question

Inverse of the statement "If $4x-1=11$, then $x=3$"

• A. If $4x-1\ne 11$, then $x\ne 3$
• B. If $4x-1\ne 11$, then $x=3$
• C. If$x=3$, then $4x-1=11$
• D. If$x\ne 3$, then $4x-1\ne 11$

Answer 1

The correct option is A If $4x-1\ne 11$, then $x\ne 3$

For any conditional staements $p\to q$
Converse statement is $q\to p$
Inverse statement is $\sim p\to \sim q$
Contrapositive statement is $\sim q\to \sim p$
So, in this case
$p\equiv$ $4x-1=11$,
$q\equiv$ $x=3$
Inverse statement is $\sim p\to \sim q$
$\Rightarrow$ If $4x-1\ne 11$, then $x\ne 3$