Conditional Statements

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Presentation transcript:

Conditional Statements

Conditionals p  q A conditional is an if-then statement. If p, then q Definition A conditional is an if-then statement. Symbolic p  q read If p, then q or p implies q Diagram q p

Rewrite the statement in if-then form. Then draw a venn diagram. Students who study do well on tests. x = 4 implies x2 = 16.

In an if-then statement, the if clause is the hypothesis, and the then clause is the conclusion.

If an animal is a robin, then the animal is a bird. Identify the hypothesis and conclusion. If an animal is a robin, then the animal is a bird.

The truth value of a conditional statement is either true or false. To show a conditional true, show every time the hypothesis is true the conclusion is also true. To show a conditional false, find ONE counterexample.

If two numbers are odd, then their sum is odd. a If two numbers are odd, then their sum is odd. a. Underline the hypothesis of the statement. b. Circle the conclusion of the statement. c. The conditional is false. Give a counterexample for the conditional statement.

The company that prints the bumper sticker at the left below accidentally reworded the original statement and printed the sticker three different ways. Suppose the original bumper sticker is true. Are the other bumper stickers true or false? Explain.

Every conditional statement has three related conditionals. If p, then q. (p  q) Converse: If q, then p. (q  p) Inverse: If not p, then not q. (~p  ~q) Contrapositive: If not q, then not p. (~q  ~p)

Given the conditional statement: If a figure is a triangle, then it is a polygon. Complete the table.

Statements with the same truth values are logically equivalent. Conditional  Contrapositive Converse  Inverse

Write a true conditional statement whose inverse is false. Get in your groups…. Write a true conditional statement that is logically equivalent to its converse. Write a true conditional statement whose inverse is false.

When both a statement and its converse are true, you can connect the hypothesis and conclusion with the words “if and only if.” This is called a bi-conditional. Determine whether the conditional statement can be written as a bi-conditional. If an animal is a fish, then it swims. If a coin is a penny, then it is worth 1 cent. If two angles are supplementary, then their sum is 180º.

All definitions you have learned can be written as “if and only if” statements. Write the definition of perpendicular lines in if and only if form.