Conditional Statements I CAN… Write conditional, converse, and biconditional statements.

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Presentation transcript:

Conditional Statements I CAN… Write conditional, converse, and biconditional statements

Conditional Statements A conditional statement is written in the form if p, then q. If a given condition is met (if p), then another condition is true or an event will happen (then q). The if-clause is the hypothesis; the then-clause is the conclusion.

Conditional Statements Ex 1.) If you don’t do your homework, then you will get lunch detention. Rewrite the statements in if-then form: Ex 2.) Every multiple of 4 is also a multiple of 2. If a number is a multiple of 4, then it is a multiple of 2. True or False? True p - Hypothesis q - Conclusion

Conditional Statements Ex. 3) True or False? False – why? Counterexample:

Converse The converse of a conditional statement is formed by switching the places of the hypothesis and conclusion. The sentence if p, then q becomes if q, then p. What is the converse?

Converse State the converse of the if-then statements: Ex. 1) If a polygon has five sides, then it is a pentagon. Converse – If a polygon is a pentagon, then it has five sides. True or False? True p - hypothesisq - conclusion p - hypothesis

Converse Ex. 2) If two lines are perpendicular, then they intersect. Converse – If two lines intersect, then they are perpendicular. True or False? False – Why? Counterexample -

Converse Ex. 3) If a college football team wins the Big Ten Conference then they will play in a bowl game. Converse – If a college football team plays in a bowl game then they won the Big Ten Conference. True or False? False – Why? Counterexample - There are many other teams that play in bowl games!

Converse Ex. 4) If you get an A on the final exam then you will get an A in Advanced Geometry. Converse – If you get an A in Advanced Geometry then you got an A on the final exam. True or False? False – Why? Counterexample - The final exam is only 15% of your grade!

Converse Ex. 5) If three points are collinear then they lie on the same line. Converse – If three points lie on the same line then they are collinear. True or False? True!

Homework p. 37 #4 – 7, 9 p. 42 #1 – 5, 8 – 12, 14