2.1 Conditional Statements

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Presentation transcript:

2.1 Conditional Statements Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3. Every prime number is odd. 4. Any three points are coplanar.

2.1 Conditional Statements Objective Recognize and analyze a conditional statement. Write postulates about points, lines, and planes using conditional statements

Example 1 Underline the hypothesis. Circle the conclusion. If today is Thanksgiving Day, then today is Thursday. A number is a rational number if it is an integer.

Example 2 Write a conditional statement from the following. An obtuse triangle has exactly one obtuse angle. b. c. Two angles that are complementary are acute.

Related Conditionals Related Conditionals

The negation of statement p is “not p,” written as ~p The negation of statement p is “not p,” written as ~p. The negation of a true statement is false, and the negation of a false statement is true. Related Conditionals

Related Conditionals

Math Journal 9-11 Symbol Words Example p  q If p, then q If the basement floor is flooded, then the basement is closed. Converse Inverse contrapositive

A conditional statement has a truth value of either true (T) or false (F). It is false only when the hypothesis is true and the conclusion is false. To show that a conditional statement is false, you need to find only one counterexample where the hypothesis is true and the conclusion is false. Related conditional statements that have the same truth value are called logically equivalent statements. A conditional and its contrapositive are logically equivalent, and so are the converse and inverse.

Then find the truth value of each. Example 3 Write the converse, inverse, and contrapositive of the conditional statement. Then find the truth value of each. Conditional: If Maria's birthday is February 29th, then she was born in a leap year. Converse: __________________________________________________________________________________________ ___________________________________________________________________________________________ Inverse: ___________________________________________________________________________________________ Contrapositive: _____________________________________________________________________________________

Note: A conditional statement is false only when the hypotheses is true and the conclusion is false. Example 4 Determine if the conditional is true. If false, give a counterexample. If this month is September, then next month is October. b. If two angles are acute, then they are congruent.

Example 5 Decide whether or not the following statement is true or false. If false, provide a counterexample. If an even number greater than 2 is prime, then 5 + 4 = 8. b. If a number is odd, then it is divisible by 3. c. If 𝑛 2 =144, then n = 12.