# Abigail Williams Characteristics

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Page 1 of 8 2.1 What you should learn GOAL 1 Recognize and analyze a conditional statement. GOAL 2 Write postulates about points, lines, and planes using conditional statements. Conditional Statements GOAL 1 RECOGNIZING CONDITIONAL STATEMENTS In this lesson you will study a type of logical statement called a conditional statement. A conditional statement has two parts, a hypothesis and a conclusion. When the statement is written in if-then form, the “if” part contains the hypothesis and the “then” part contains the conclusion. Here is an example: If it is noon in Georgia, then it is 9 A.M. in California. Hypothesis Conclusion Why you should learn it Point, line, and plane postulates help you analyze real-life objects, such as the research buggy below and in Ex. 54. AL LI RE EXAMPLE 1 Rewriting in If-Then Form Rewrite the conditional statement in if-then form. a. Two points are collinear if they lie on the same line. b. All sharks have a boneless skeleton. c. A number divisible by 9 is also divisible by 3. SOLUTION a. If two points lie on the same line, then they are collinear. b. If a fish is a shark, then it has a boneless skeleton. c. If a number is divisible by 9, then it is divisible by 3. E FE .......... Conditional statements can be either true or false. To show that a conditional statement is true, you must present an argument that the conclusion follows for all cases that fulfill the hypothesis. To show that a conditional statement is false, describe a single counterexample that shows the statement is not always true. Coastal Research Amphibious Buggy EXAMPLE 2 Writing a Counterexample Write a counterexample to show that the following conditional statement is false. If x 2 = 16, then x = 4. SOLUTION As a counterexample, let x = º4. The hypothesis is true, because (º4)2 = 16. However, the conclusion is false.