![]() Remember that a conditional statement has a one-way arrow ( ) and a biconditional statement has a two-way arrow ( ). Note that in the biconditional above, the hypothesis is: "A polygon is a triangle" and the conclusion is: "It has exactly 3 sides." It is helpful to think of the biconditional as a conditional statement that is true in both directions. The statement p q represents the sentence, "A polygon is a triangle if and only if it has exactly 3 sides." In the truth table above, p q is true when p and q have the same truth values, (i.e., when either both are true or both are false.) Now that the biconditional has been defined, we can look at a modified version of Example 1. The following is a truth table for biconditional p q. The biconditional p q represents "p if and only if q," where p is a hypothesis and q is a conclusion. The biconditional operator is denoted by a double-headed arrow. When we combine two conditional statements this way, we have a biconditional.ĭefinition: A biconditional statement is defined to be true whenever both parts have the same truth value. In the truth table above, when p and q have the same truth values, the compound statement (p q) (q p) is true. Let's look at a truth table for this compound statement. In the first conditional, p is the hypothesis and q is the conclusion in the second conditional, q is the hypothesis and p is the conclusion. ![]() The compound statement (p q) (q p) is a conjunction of two conditional statements. ![]() Given:ĭetermine the truth values of this statement: (p q) (q p) ![]() Biconditional Statement Problems With Interactive ExercisesĮxample 1: Examine the sentences below. ![]()
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