From premises A ⇒ B and B ⇒ A, conclude B' + A.B.

(i) Let P : He has fax and Q : He uses e-mail.
Write the following statement in terms of P and Q:
He has fax and he may or may not use e-mail.

Let X=1 represents "you work hard" and 0 otherwise.
Let Y=1 represents "you succeed" and 0 otherwise.
Using the information given above, construct:
(i) the truth table and
(ii) the logical expression for the following statement:
"If and only if you work hard you succeed".

Draw the truth table to prove the following proportional expression:

a ⇒ b = (a ⇒ b) . (b ⇒ a)