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Writ the converse, inverse and contrapos...

Writ the converse, inverse and contrapositive of each of the following statements :
(1) A family becomes literate if the women in it are literate.
(2) If it rains, then the match will be cancelled.

Text Solution

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(1) Let p : The women in the family are literate.
q : A family becomes literate.
Then the symbolic form of the given statement is `ptoq`.
Convers : `qtop` is the converse of `ptoq`
i.e., if a family becomes literate, then women in it are literate.
Inverse : `~pto~q` is the inverse of `ptoq`
i.e., If the women in the family are not literate, then family does not become literate.
Contrapositive : `~qto~p` is the contrapositive of `ptoq`
i.e., If a family does not become literate, then the women in it are not literate.
(2). Let p : It rains.
q: The match will be cancelled.
Then the symoblic form of the given statement is `ptoq`
Converse : `qtoq` is the converse of `ptoq`
i.e., If the match is cancelled, then it rains.
Inverse : `~pto~q` is the inverse of `ptoq`
i.e., If it does not rain, then the match will not be concelled.
Contrapositive : `~qto~p` is the contrapositive of `ptoq`
i.e., If the match is not cancelled, then it does not rain.
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