Question

The contrapositive of “if x has courage then x will win”, is:
A) If x will win, then x has the courage
B) If x has no courage, then x will not win.
C) If x will not win, then x has courage.
D) If x will not win, then x has courage.

Answer 1

Firstly we should know what is a contrapositive proposition. A proposition or theorem termed by contradicting both the subject and predicate or both the hypothesis and the conclusion of a given proposition or theorem and interchanging them.

Complete step by step solution: Now let's move to the solution. In these types of questions, we should first assign variables to both the subject and the predicate.
Its assume:
P: x has courage (hypothesis)
q: x will win (conclusion)
Now we have the final contraposition of this.
By definition, the contrapositive of $p \Rightarrow q$ is $\sim q \to \sim p$
$\sim q$ (inverse q) will be “x will not win.”
$\sim p$ (inverse p) will be “x has no courage”.
Thus applying above definition, we get
$\sim q \to \sim p$
“If x will not win, then x has no courage”
Option B which is our solution.

Note: While solving such questions, the most important thing is to split the proposition into hypothesis and conclusion, then assign them some variables (line p, q etc.) then apply the required formula to compute.