Question

The contrapositive of "if $x$ has courage then $x$ will win", is

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

Take $p:x$ has courage

and $q:x$ will win

So the given conjugation is $p\Rightarrow q$

Now we need to find Contrapositive of this.

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

$\sim q:x$ will not win and

$\sim p:x$ has no courage

Thus the Contrapositive $\sim q⟶\sim p$ is symbolic for "if $x$ will not win, then $x$ has no courge"