CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015.

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Presentation transcript:

CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015

 I can identify, write, and analyze the truth value of conditional statements.  I can write the inverse, converse, and contrapositive of a conditional statement.

Definitions  Conditional Statement - a statement that can be written in the form “if p, then q.”  Hypothesis – the part p of a conditional statement following the word if.  Conclusion – the part q of a conditional statement following the word then.

Venn Diagram

Practice Birds Sparrows Stringed Instruments Violin If an animal is a sparrow, then it is a bird. If an instrument is a violin, then it is a stringed instrument.

Identify:  Identify the hypothesis and conclusion  A number is divisible by 3 if it is divisible by 6.  If today is Thanksgiving Day, then today is Thursday.  A number is a rational number if it is an integer.

Truth Value  A conditional statement has a truth value of either true (T) or false (F).  If I get paid, I will take you to the movie.  If I don’t get paid, I haven’t broken my promise. SO the statement is still true.  To show a conditional statement is false, you need only one counterexample where the conclusion is false.

Truth Value of a Conditional Statement  If a number is odd, then it is a divisible by 3.  True or false? Counterexample?  If this month is August, then next month is September.  If two angles are acute, then they are congruent. F T F

Related Conditionals

Examples  Converse: If an animal has 4 paws, then it is a cat.  Inverse: If an animal is not a cat, then it does not have 4 paws.  Contrapositive: If an animal does not have 4 paws, then it is not a cat. F F T

Logically Equivalent Statements  Related conditional statements that have the same truth value  A conditional and its contrapositive are logically equivalent.  A converse and its inverse are logically equivalent. The logical equivalence of a conditional and its contrapositive is known as the Law of Contrapositive.