Conditional Statements

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Presentation transcript:

Conditional Statements 1-3 We will… Identify and determine the validity of the converse, inverse, and contrapositive

If an animal has feathers, then it is a bird. I will go to the movies if I finish my homework. If a vehicle is built to fly, then it is an airplane.

If it is sunny, then I will go to the park Conditional statement- if-then statement Hypothesis- if-clause Conclusion- then-clause If it is sunny, then I will go to the park q p

Different forms of conditional statements: If p, then q p implies q q if p

Counterexample- example that can be found for which the hypothesis is true and the conclusion is false Proving something is false Only need one to prove something is false

Converse- interchanging the hypothesis and the conclusion Conditional: if p then q Converse: if q then p

Inverse- negating both the hypothesis and conclusion Conditional: if p then q Inverse: if not p then not q

Contrapositive- interchanging and negating the hypothesis and the conclusion Conditional: if p then q Contrapositive: if not q then not p

T F F T Square Rectangle Write the statement True or false? If false, give counter-example Conditional statement If a figure is a triangle, then it is a polygon. Converse Inverse Contrapositive T If a figure is a polygon then it is a triangle. F Square If a figure is not a triangle, then it is not a polygon. F Rectangle If a figure is not a polygon, then it is not a triangle. T

Logically equivalent- Statements that have the same truth value Biconditional statement- when a statement and its converse are both true “if and only if” Most definitions Example: if two lines intersect at 90 degrees, then they are perpendicular.

“Numbers that do not end in 2 are not even” Example: “Numbers that do not end in 2 are not even” If-then: Converse: Inverse: Contrapositive: Can you write it as a biconditional? If numbers do not end in 2, then they are not even. If numbers are not even, then they do not end in 2. If numbers end in 2, then they are even. If numbers are even, then they end in 2. No!