For example, the implication If she is inside the house, then she cannot see the moon does not have the same meaning as its converse statement If she cannot see the moon, then she is inside the house . If the tank is full, then we have enough water . We have enough water only if the tank is full . Her right shoe is black . Statements such as these are called equivalence statements.
Today is a weekday .
If and Only If In an equivalence statement, the words if and only if may be represented by the short symbol iff . Here the first implication means that when p is true, q must be true, and we cannot have p true and q false. The second implication means that when q is true, p must be true, and we cannot have q true and p false. Then p and q are said to be equivalent . Next month is June .