Question

The inverse of "If $x$ has courage, then $x$ will win", is

• A. If $x$ will win, then $x$ has courage.
• B. If $x$ has no courage, then $x$ will not win.
• C. If $x$ will not win, then $x$ has no courage.
• D. If $x$ will not win, then $x$ has courage.

Answer 1

The correct option is B If $x$ has no courage, then $x$ will not win.

Take $p:x$ has courage

and $q:x$ will win

So the given conjugation is $p\Rightarrow q$

Now we need to find Inverse of this.

Be definition, Inverse of $p\Rightarrow q$ is $\sim p⟶\sim q$

$\sim p:x$ has no courage and

$\sim q:x$ will not win

Thus the inverse $\sim p⟶\sim q$ is symbolic form of "If $x$ has no courage, then $x$ will not win.