Conditional Statements SECTION 10.3 MAY 15/16 GOAL: TO LEARN ABOUT AND USE CONDITIONAL STATMENTS IN There is a law that states... “If your windshield wipers are on, then your headlights must be on.” Or If wipers Then headlights Assume the original statement is true…. Which, if any, MUST also be true? If headlights Then wipers If no wipers Then no headlights If no headlights Then no wipers • A Conditional is an if-then statement • The part that follows “if” is the Hypothesis( p ) • The part that follows “then” is the Conclusion (q) Identify the Hypothesis and Conclusion of the following: conclusion (q) hypothesis (p) If an animal is a robin, then the animal is a bird. Note: Do not include the words “if” or “then.” hypothesis (p) conclusion (q) If an angle measures 130 degrees, it is obtuse. hypothesis (p) conclusion (q) Two points are collinear if they lie on the same line. Re-write the following conditional statements in if-then form. Then identify the Hypothesis (p) and Conclusion (q) of the following: 1. An object weighs one ton if it weighs 2000 pounds. If an object weighs 2000 pounds, then it weighs one ton. conclusion (q) hypothesis (p) 2. *A fish can swim. If an animal is a fish, then it can swim. hypothesis (p) conclusion (q) Write a conditional statement to represent each Venn diagram. If a number is a whole number then it is an integer. If a food is a wheat product then it is a grain. Is the conditional true or false? If it is false, find a counterexample. If a number is divisible by three, then it is odd. 1. • False - 12 is divisible by three and twelve is even If a month has only 28 days, then it is February. 2. • True If two angles form a linear pair, then they are supplementary. 3. • True If an animal has spots, then it is a leopard 4. • False- Dalmatians have spots and they are not leopards. To negate a statement, write the negative or opposite of that statement 1. Brenda likes pizza. Negation: Brenda does not like pizza. 2. Monkeys eat bananas. Negation: Monkeys do not eat bananas. 3. Ben does not play tennis. Negation: Ben plays tennis. …When you negate the hypothesis and the conclusion ~p ~q Write the inverse of the following statements. 1. If it rains, practice will be canceled. Inverse: If it does not rain, practice will not be cancelled. 2. If the battery is not charged, then the car will not start. Inverse: If the battery is charged, then the car will start. …Switch the hypothesis and conclusion qp 1. Write the converse of each statement. If you see lightening, then you hear thunder Converse: If you hear thunder, then you see lightening 2. If Allen gets a summer job, then he will bay a car. Converse: If Allen buys a car, then he will get a summer job. …Switch and negate the hypothesis and conclusion. ~q ~p 1. If it is raining, I will go to the movies Contrapositive: If I do not go to the movies, then it is not raining. 2. If the sun is out, then the weather is good. Contrapositive: If the weather is not good, then the sun is not out. 3. If a figure is a triangle, then it has three sides. Contrapositive: If a figure does not have three sides, then it is not a triangle. Write the converse, inverse, and contrapositive and state whether each is true or false. If false, provide a counterexample. Original Conditional: If a figure is a square, then it is a quadrilateral. True Converse: If a figure is a quadrilateral, then it is a square. False; A rectangle is a quad but is not a square. Inverse: If a figure is not a square, then it is not a quadrilateral. False; A rectangle is not a square but is a quad. Contrapositive: If a figure is not a quadrilateral, then it is not a square. True Notice that the Original and Contrapositive have the same truth value, and the Converse and Inverse have the same truth value. Conditional Inverse Converse Contrapositive pq ~p ~q qp ~q ~p
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