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The contrapositive of the statement: "If...

The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic".

A

The weather is fine but my friends will not come or we do not go for a picnic

B

if my friends do not come or we do not go for picnic then weather will not be fine

C

If the weather is not fine then my friends will not come or we do not go for a picnic

D

The weather is not fine but my friends will come and we go for a picnic

Text Solution

Verified by Experts

The correct Answer is:
B
Given statement is
"I the weather is fine then my friends will come and we go for a picnic".
Here, p=the weather is fine
q=my friends will come
r=we go for a picnic
Symbolic form is `p to (q ^^ r)`
contrapositive of `p to q` is `~q ^^ ~ p`
`therefore ` contrapositive of `p to (q ^^ r)~ (q ^^ r)~p`
`implies(~q vv ~ r) to ~p`
`therefore` Contrapositive of the given statement is, if my friends will not come or we do not go for a picnic then weather will not fine.
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