Question

All couples who have children are happy All couples either have children or are happy Assuming...

All couples who have children are happy
All couples either have children or are happy
Assuming the above to be true, which of the following cannot be true?
a. All couples are happy.
b. Some couples who are happy have children.
c. Some couples who have children are not happy.
d. Some couples have happy children.
e. Children of happy couples are happy.

Math   Statistics-And-Probability   
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Answer #1

Answer:-

(a)All couples are happy

This statement is TRUE according to given statements.

(b)Some couples who are happy have children

According to given statement all couples are happy who have children not some couples.

This statement is FALSE according to given statements.

(c)Some couples who have children are not happy

According to given statement all couples either have children or are happy

This statement is FALSE according to given statements.

(d)Some couples have happy children

This statement is not related to the given statements.

So,It is FALSE.

(e) Children of happy couples are happy.

This statement is TRUE.

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