Statements that are Conditional with a hypothesis and a conclusion. The If part of the statement is the Hypothesis, and the Then part of the statement.

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Presentation transcript:

Statements that are Conditional with a hypothesis and a conclusion. The If part of the statement is the Hypothesis, and the Then part of the statement is the Conclusion. If you are a champion then you are afraid to lose. A Champion is afraid to lose.

Examples StatementIf-Then Form Babies are small.If a person is a baby, then they are small. A triangle has three sides. If a shape is a triangle, then it has three sides. Snakes are despised.If an animal is a snake, then it is despised.

If the sun is up then it is morning. If the sun is up then it can be in the afternoon. Conditional Statements have a truth value, of true or false. To prove that a statement is false it only takes one counterexample which shows that the hypothesis is true and the conclusion is false.

A Venn diagram can be used to illustrate conditional statements. If you live in Chicago, then you live in Illinois. Residents of Illinois Residents of Chicago

Take the original statement and switch the hypothesis and the conclusion. Conditional If two points are on the same line, then they are collinear. Converse If two points are collinear, then they are on the same line.

Conditional If two lines intersect to form right angles, then they are perpendicular. Converse If two lines are perpendicular, then they intersect to form right angles. Conditional If something is a cocker spaniel, then it is a dog. Converse If something is a dog, then it is a cocker spaniel. More Examples Symbolic Form p → q q → p You Read it If p, then q. If q, then p.

When a conditional and its converse are true, you can combine them as a true biconditional. Conditional If two angles have the same measure, then they are congruent. Converse If two angles are congruent, then they have the same measure. Biconditional Two angles have the same measure if and only if (iff ) the angles are congruent. p q

Conditional If an angle is a straight angle, then its measure is 180º. Converse If an angle has a measure of 180º, then it is a straight angle. Biconditional An angle is a straight angle if and only if (iff) its measure is 180º. Example: Symbolic Form: You read it: p → q If p then q. Symbolic Form: You read it: p q p if and only if q. Symbolic Form: You read it: q → p If q then p.