2.2 Conditional Statements You can describe some mathematical relationships using a variety of if-then statements. A conditional – an if-then statement.

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Presentation transcript:

2.2 Conditional Statements You can describe some mathematical relationships using a variety of if-then statements. A conditional – an if-then statement. symbol: p  q read as “if p then q” or “p implies q”. Hypothesis – the “if” part of the statement. Conclusion – the “then” part of the statement. Venn diagrams – show how the set of things that satisfy the hypothesis lies inside the set of things that satisfy the conclusion.

Identifying the Hypothesis and the Conclusion What are the hypothesis and the conclusion of the conditional? If an animal is a robin, then the animal is a bird. Hypothesis (p): an animal is a robin. Conclusion (q): the animal is a bird.

Writing a Conditional How can you write the following statement as a conditional? Vertical angles share a vertex. Step 1 – identify the hypothesis and the conclusion. Vertical angles share a vertex. Step 2 – write the conditional. If two angles are vertical, then they share a vertex.

Truth Value The truth value of a conditional is either true or false. – To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true. – To show a conditional is false, find only one counterexample for which the hypothesis is true and the conclusion is false.

Finding the Truth Value of a Conditional Is the conditional true or false. If it is false, find a counterexample. A.If a woman is Hungarian, then she is European. B.If a number is divisible by 3, then it is odd.

Finding the Truth Value of a Conditional Is the conditional true or false. If it is false, find a counterexample. A.The conditional is true. Hungary is a European nation, so Hungarians are European. B.The conditional is false. The number 6 is divisible by 3, but it is not odd.

Negation The negation of a statement p is the opposite of the statement. – The symbol is ~p and is read “not p”. – Ex. The negation of “the sky is blue” is “the sky is not blue.” – You can use negations to write statements related to a conditional. Every conditional has 3 related conditional statements.

Equivalent Statements Equivalent statements have the same truth values. – Conditional and contrapositive – equivalent statements. They are either both true or both false. – Converse and inverse – equivalent statements.

Writing and Finding Truth Values of Statements See example 4 on p. 92.

More Practice!!!!! Homework – Textbook p. 93 # 5 – 24 ALL.