What is a Biconditional Students will be able to: 1.Rewrite compound sentences in conditional form 2.Find the biconditional of a conditional 3.Tell when/why.

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Presentation transcript:

What is a Biconditional Students will be able to: 1.Rewrite compound sentences in conditional form 2.Find the biconditional of a conditional 3.Tell when/why a biconditional is true

Why is the following statement called a hidden conditional? “My parents get mad when I don’t do my homework” The hypothesis and a conclusion are hidden. “If I don’t do my homework, then my parents get mad

If a polygon has four sides, then the shape is a quadrilateral p: A polygon has four sides q: The shape is a quadrilateral If a polygon has four sides then the shape is a quadrilateral and if the shape is a quadrilateral then the polygon has four sides A polygon has four sides if and only if the shape is a quadrilateral 1) Write p  q in words 2) Write q  p in words If the shape is a quadrilateral, then the polygon has four sides Write in words 3)

What is a biconditional?

A polygon has four sides if and only if the shape is a quadrilateral. This type of statement is called a biconditional. A biconditional is formed by combining two simple statements using the words “if and only if”. Symbol: p q Definition:

p: School is not in session q: It is the weekend. Write the biconditional statement in words. School is not in session if and only if it is the weekend.

pqp qq p T T T T T T T T T T T T F FF F F F F F A biconditional is true when p and q have the same truth values p q General Truth Table for a BICONDITIONAL (p q) (q p ) T T= T F F= T

p: The car stops q: There is a red light Write the biconditional statement in words. The car stops if and only if there is a red light This biconditional statement is FALSE because “If the car stops then there is a red light,” is not always true.

p: A polygon has four right angles q: A polygon is a square 3. Create a biconditional statement A polygon has four right angles if and only if it is a square 1. Translate p  q in words If a polygon has four right angles then it is a square 2. Translate q  p in words If a polygon is a square then it has four right angles Note:

Regents Prep Logic Website /PracAnd.htm

1) What is the symbol for a biconditional? 2) When is a biconditional true?