Part 2 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.

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Presentation transcript:

Part 2 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

Related Conditional Statements StatementHow To WriteExampleSymbolHow to read ConditionalUse the given hypothesis and conclusion If m<A = 15, then <A is acute p  qIf p, then q ConverseExchange the hypothesis and conclusion If <A is acute, then m<A = 15 q  pIf q, then p InverseNegate both the hypothesis and conclusion from the conditional If m<A ≠ 15, then <A is not acute ~p  ~ qIf not p, then not q Contrapositiv e Negate both the hypothesis and conclusion from the converse If <A is not acute, then m<A ≠ 15 ~q  ~pIf not q, then not p

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 ContrapositiveIf <A is not acute, then m<A ≠ 15 True 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!