Conditional & Biconditional Statements Chapter 2 Section 2 1.

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Presentation transcript:

Conditional & Biconditional Statements Chapter 2 Section 2 1

HypothesisConclusion IF then Examples: If it is a nice day then I will go to the park Conditional Statements an “if-then” statement Symbolic Notation p  q (If p then q) q  p (If q then p) 2

Converse The converse of a conditional switches the hypothesis and the conclusion. Example Conditional: If 2 lines intersect to form right angles then they are perpendicular. Converse: If 2 lines are perpendicular then they intersect to form right angles. 3

Truth Value A conditional statement can have a truth value of true or false. To show a conditional is TRUE Show that every time the hypothesis is true, the conclusion is true To show a conditional is FALSE Find a counterexample in which the hypothesis is TRUE and the conclusion is FALSE 4

Conditional: If a figure is a square then it has 4 sides. True or False? Converse: If a figure has 4 sides then it is a square. True or False? Example 5

Write the converse of the conditional statement. a) If an angle has less than 90 degrees, then it is an acute angle. b) If a figure has four congruent sides, then it is a square. Practice 6

Biconditional Statement the combination of a conditional statement and its converse (as long as both statements are true). statements are combined using the phrase “if and only if” (iff) Example: Two angles have the same measure if and only if the angles are congruent. 7

Symbolic Form StatementExampleSymbolic FormRead Conditional If there is lightning, then there is thunder. p→qp→qIf p, then q Converse If there is thunder, then there is lightning. q→pq→pIf q, then p Biconditional There is lightning if and only if there is thunder. p↔qp↔qp iff q 8

Conditional: If three points are collinear, then they lie on the same line. Converse: If three points lie on the same line, then they are collinear. Biconditional: Example Write the biconditional: 9

Biconditional: A number is divisible by 3 if and only if the sum of its digits is divisible by 3. Conditional: Converse: Separate the biconditional into two conditional statements. Example 10

Venn Diagrams A Venn diagram can represent a conditional statement: –p: A figure is a quadrilateral. –q: A figure is a square. p q –p: A figure is a quadrilateral. –q: A figure is convex. What does the intersection represent? pq 11

Venn Diagrams Draw a Venn Diagram below for each of the following statements: a. All squares are rhombi. b. Some rectangles are squares. c. No trapezoids are parallelograms. 12