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Conditional Statements. Section 2-2. Objective. Students will be able to recognize conditional statements and their parts to write converses, inverses, and contrapositives of conditionals. Conditional Statements. If-then statements are called conditional statements.
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Conditional Statements Section 2-2
Objective Students will be able to recognize conditional statements and their parts to write converses, inverses, and contrapositives of conditionals.
Conditional Statements If-then statements are called conditional statements. The portion of the sentence following if is called the hypothesis. The part following then is called the conclusion. p q (If p, then q)
p q If it is an apple, then it is a fruit. Hypothesis – It is an apple. Conclusion – It is a fruit. A conditional can have a truth value of true or false.
Converse q p The converse statement is formed by switching the hypothesis and conclusion. If it is an apple, then it is a fruit. Converse: If it is a fruit, then it is an apple. The converse may be true or false.
Underline the hypothesis and circle the conclusion for each conditional statement, then write the converse. • If you are an American citizen, then you have the right to vote. • If a figure is a rectangle, then it has four sides.
Write each sentence as a conditional statement. • A point in the first quadrant has two positive coordinates. If a point is in the first quadrant, then it has two positive coordinates. • Thanksgiving in the U.S. falls on the fourth Thursday of November. If it is Thanksgiving in the U.S., then it is the fourth Thursday of November.
Using a Venn Diagram to illustrate a conditional Illinois Residents Chicago Residents If you live in Chicago, then you live in Illinois.
Get a Partner! • Each of you need to write 5 conditional statements and draw 5 venn diagrams • Trade papers • Write the converse of each conditional statement your partner wrote.
Biconditionals • Remember: If your original conditional statement is true and your converse is true, then you can write a biconditional. p↔q read as “p if and only if q” we can shorten it to “p iff q”. • When either or both of your condition and the converse is false, then you must write a counter example. Why is it false? • See page 78 for sample problems!
The new stuff for today: negation – the denial of a statement (the opposite) Ex. “An angle is obtuse.” Negation – “An angle is not obtuse.”
Inverse ~p ~q An inverse statement can be formed by negating both the hypothesis and conclusion. If it is an apple, then it is a fruit. Inverse: If it is not an apple, then it is not a fruit. The inverse may be true or false.
Contrapositive ~q ~p A contrapositive is formed by negating the hypothesis and conclusion of the converse. If it is an apple, then it is a fruit. Contrapositive: If it is not a fruit, then it is not an apple. The contrapositive of a true conditional is true and of a false conditional is false.
Truth Table T F T T T F T T T T F T T T F T T F F F T T T F T T T F F T F F Which columns are congruent? These are called equivalent statements, because they have the same truth values!
Assignment: • P. 93 (15-45) x’s of 3 • Ask me about the OPTIONAL project!
