MATH: IF-THEN STATEMENTS

• Conditional statements express conditions. It can be written in "if-then" form
• Conditional statements are also called if-then statements
• The subject of the original sentence is to be found in the "if" part; the predicate is in the "then" part.
• A conditional statement has hypothesis and conclusion. The part of a conditional statement after "if" contains the hypothesis and the part after the "then" contains the conclusion.
• The hypothesis and the conclusion are sentences.
• A conditional statement is false when the conclusion is false and the hypothesis is true. Otherwise, the conditional is true.
• Counterexample is used to justify that a given conditional is false. It could be a figure, an explanation, or a situation.
• The general form of a conditional is "If p, then q." The hypothesis is p and the conclusion is q.
• Negation of the p-statement: not p, in symbol, ~ p Negation of the q-statement: not q, in symbol, ~q
• A statement can be negated by using the word "not"
• Conditional: If p, then q. When interchanged: If q, then p. When both negated: If ~p, then~q. When both negated and interchanged: If~q, then~p.
• When p-statement and q-statement of a conditional are interchanged, the resulting statement is called the converse of the given conditional.
• When p-statement and q-statement of a conditional are both negated, the resulting statement is called the inverse of the given conditional.
• When p-statement and q-statement of a conditional are both negated and interchanged, the resulting statement is called the contrapositive of the given conditional.
• When a conditional and its converse are both true, another statement can be formed. This statement is called biconditional. It uses the phrase "if and only if." A biconditional statement has the form p if and only if q. The shorter form of if and only if is iff. All definitions of terms can be written as biconditional.
• A conditional statement may be true or false
• Definition of terms may be written as biconditionals