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Let p and q are two statements then "if p then q" is a compound statement, denoted by p→ q and referred as a conditional statement, or implication. The implication p→ q is false only when p is true, and q is false; otherwise, it is always true. In this implication, p is called the hypothesis (or antecedent) and q is called the conclusion (or consequent).
For Example: The followings are conditional statements.
- If a = b and b = c, then a = c.
- If I get money, then I will purchase a computer.
If p and q are two statements then "p if and only if q" is a compound statement, denoted as p ↔ q and referred as a biconditional statement or an equivalence. The equivalence p ↔ q is true only when both p and q are true or when both p and q are false.
(i) Two lines are parallel if and only if they have the same slope.
(ii) You will pass the exam if and only if you will work hard.