Conditional Statements Learning Target: I can write converses, inverses, and contrapositives of conditionals.

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Presentation transcript:

Conditional Statements Learning Target: I can write converses, inverses, and contrapositives of conditionals.

·Conditional Statements are If-Then Statments Ex. If you are not completely satisfied, then your money will be refunded. ·Hypothesis - the part following the If Ex. you are not completely satisfied ·Conclusion - the part following the Then Ex. your money will be refunded.

The letter p always represents the hypothesis. The letter q always represents the conclusion. Notation: p q For a conditional, we say if p then q. Ex. If m<A=15, then <A is acute.

Identify the hypothesis and conclusion If today is September 23, then it is Ms.Tilton's birthday Hypothesis: Conclusion: Today is September 23 It is Ms. Tilton's birthday

Identify the hypothesis and the conclusion of the conditional. If an angle measures 130, then the angle is obtuse. Hypothesis: Conclusion: An angle measures 130 The angle is obtuse.

Writing a Conditional A rectangle has four right angles Ex. If a figure is a rectangle, then is has foud right angles. A tiger is an animal Ex. If something is a tiger, then it is an animal. A square has four congruent sides Ex. If a figure is a square, then it has four congruent sides.

·Truth value - whether a conditional is true of false ·To show a conditional is true, show that every time the hypothesis is true, the conclusion is also true. ·To show a conditional is false, you need to find a counter example.

Find a counterexample for these conditionals ·If it is February, then there are only 28 days in the month. ·If an animal is a dog, then it is a beagle. Leap Year! Poodles are dogs, but not beagles.

Is the conditional true or false? If it is false, find a counterexample. Ex. If a woman is Hungarian, then she is European. Ex. If a number is divisible by 3, then it is odd. A woman can be from France and still be European. 6 is divisible by 3, but not odd.

·The converse of a conditional switches the hypothesis and the conclusion. ·Write the converse of the following conditionals. 1. If two lines intersect to form right angles, then they are perpendicular. Converse:If two lines are perpendicular, then they intersect to form right angles. 2. If two lines are perpendicular, then they intersect to form right angles. Converse: If two lines intersect to form right angles, then they are perpendicular.

Notation: q p For a converse, we say if q then p. Conditional: If m<A=15, then <A is acute. Converse: If <A is acute, then m<A=15.

Find the Truth Value of a Converse Ex. Write the Converse and determine its truth value. If a figure is a square, then it has four sides. If a figure has four sides, then it is a square. False, a rectangle has four sides, but is not a square.

The negation of a statement has the opposite truth value. The symbol ~ is used to represent negation. Write the negation of each statement. a. <ABC is obtuse. b. Today is not tuesday. c. Lines m and n are perpendicular. <ABC is not obtuse Today is Tuesday.

The inverse of a conditional statement negates both the hypothesis and the conclusion. Notation: ~p ~q We read this If not p, then not q. Conditional: If m<A=15, then <A is acute. Inverse: If m<A≠15, then <A is not acute.

Write the inverse of these conditionals: a. If a figure is a square, then it is a rectangle. b. If an angle measures 90, then it is a right angle. If a figure is not a square, then it is not a rectangle. If an angle does not measure 90, then it is not a right angle.

The contrapositive of a conditional switches the hypothesis and the conclusion and negates both. Notation: ~q ~p We read this as if not q, then not p. Contional: If m<A=15, then <A is acute. Contrapositive: If <A is not acute, then m<A≠15.

Write the contrapositive of these conditionals: a. If a figure is a square, then it is a rectangle. If a figure is not a rectangle, then it is not a square. b. If an angle measure 90, then it is a right angle. If an angle is not right, then it does not measure 90.

Equivalent statements have the same truth value. StatementExampleTruth Value ConditionalIf m<A=15, then <A is acute. True ConverseIf <A is acute, then m<A=15. False InverseIf m<A≠15, then <A is not acute. False Contrapositi ve If <A is not acute, then m<A≠15. True