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## Part 2

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**Part 2**Conditional Statements**Conditional Statements**• A conditional is an If – then statement • p q (read as if p then q or p implies q) • The Hypothesis is the part p following if • The Conclusion is the part q following then.**Identifying the Hypothesis and Conclusion**• What is the hypothesis and conclusion of the conditional? • If an animal is a robin, then the animal is a bird • H – An animal is a robin • C – The animal is a bird • If an angle measures 130, then the angle is obtuse • H – An angle measures 130 • C – The angle is obtuse**Writing a Conditional**• Write the following statement as a conditional • Vertical angles share a vertex • Step 1: Identify the Hypothesis and Conclusion • H: Vertical Angles • C: Share a vertex • Step 2: Write the Conditional • If two angles are vertical, then they share a common vertex • You Try: How can you write “Dolphins are mammals” as a conditional? • If an animal is a dolphin, then it is a mammal**Truth Value**• The truth value of a conditional is either true or 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 find one counter example for which the hypothesis is true and the conclusion is false**Finding the Truth Value of a Conditional**• Is this conditional true or false, if it is false find a counter example. • If a women is Hungarian, then she is European. • This is True! • If a number is divisible by 3, then it is odd. • This is false, the number 12 is divisible by three and not odd. • If a month has 28 days than it is February • This false, January has 28 days • If two angles form a linear pair, then they are supplementary • True!**Negation**• The negation of a statement p is the opposite of that statement, the symbol is ~p and is read “not p” • Example: • The negations of the statement “the sky is blue” is “the sky is not blue” • You use the negation to write statements related to a condition**Truth Value**Equivalent Statements have the same truth value, the conditional and contrapositive are equivalent, and are the converse and inverse statements.**You Try**• Write the Converse, Inverse and Contrapositive statements • IF a vegetable is a carrot, then it contains beta carotene • Converse • If a vegetable contains beta carotene then it is a carrot • False (Spinach has Beta Carotene) • Inverse • If a vegetable is not a carrot then it does not contain beta carotene • False • Contrapositive • If a vegetable does not contain beta carotene then it is not a carrot • True!