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Question
Write converse, inverse and contrapositive of the following statement.
A family becomes literate if the woman in it is literate.
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Solution
Let p: The woman in the family is literate.
q: A family becomes literate.
Then the symbolic form of the given statement is p → q.
Converse: q → p is the converse of p → q.
i.e. If a family becomes literate, then the woman in it is literate.
Inverse: ∼p → ∼q is the inverse of p → q.
i.e. If the woman in the family is not literate, then the family does not become literate.
Contrapositive: ∼q → ∼p is the contrapositive of p → q.
i.e. If a family does not become literate, then the woman in it is not literate.
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