Question

Write the converse, inverse and contrapositive of the following statement :
A family becomes literate if the women in it are literate.

Answer 1

Let p: The woman in the family is literate.
Let q: A family becomes literate.
Then the symbolic form of the given statement is $p\to q$.
Converse: $q\to p$ is the converse of $p\to q$.
i.e., If a family becomes literate, then the woman in it is literate.
Inverse: $\sim p\to \sim q$ is the inverse of $p\to q$.
i.e., If the woman in the family does not become literate.
Contrapositive: $\sim q\to \sim p$ is the contrapositive of $p\to q$.
i.e., If a family does not become literate, then the woman in it is not literate.