forming statements

Question

 a) Choose two simple English propositions and form a conditional statement from them using “only if”.

b) Write the inverse, converse and contrapositive of your conditional statement.

c) Write the inverse of the inverse, the converse of the converse and the contrapositive of the contrapositive of your original statement.

Hint: There should be seven sentences in total.

Answer 1

you give us the statement only if we will provide the answers.

Inverse:

you do not giove us the statement only if we do not provide the answers

Converse:

we provide the answers only if you give the statement

Contrapositive:

We do not provide the answer only if you do not give the statement.

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If you give us the statement, then we provide the answers:

inverse: if you do not give the statement then we do not provide the answers

converse: if we provide the answers then you give the statement

contrapositive: if we do not provide the answers then you do not give the statement

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If we provide the answers then you give us the statement

inverse: if we do not provide the answers then you did not give us the statement

converse: if you give us the statement then we provide the answers

contrapositive: if we did not provide the answers then you did not give us the statement

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P->Q = if P then Q

inverse: not P --> not Q = if not P then not Q

converse: if Q then P

converse if not Q then not P = not Q --> not P