15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part.

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15) 17) 18) ) 23) 25)

Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part is the hypothesis; the “then” part is the conclusion. If it is noon in Georgia, then it is 9 A.M. in California. hypothesis conclusion Conditional statements can be either true or false. To show that a conditional statement is true, you must prove that for EVERY POSSIBLE case that satisfies the hypothesis, the conclusion is valid. To prove that a conditional statement is false, a single counterexample where the hypothesis is true but the conclusion is invalid is enough proof.

 All ducks are soft.  The city you visited, Phoenix, is the capital of Arizona.  On Tuesdays, Ms. McEwen assigns Science homework.

Write a counterexample to show that the following conditional statement is false. SOLUTION Think of a case where x 2 = 16 There are 2: x = – 4 and x = 4. However, when x = – 4, the conclusion is false (if x = – 4 then it can’t = 4). This means the given conditional statement is false. If x 2 = 16, then x = 4.

 When verifying true conditional statements, there are some links!  If the original statement is true, its contrapositive will also be true.  If the converse of a statement is true, its inverse will also be true.

 For each statement, do the following: a) Rewrite as a conditional statement. b) Determine if it is true. c) Determine which of the other statements (inverse, converse, contrapositive) are also true. Statement 1: All CPA 9 th Grade students wear black socks. Statement 2: A student who earns 95% has an A. Statement 3: All lines contain at least two rays. Statement 4: For every integer value of x less than 4, x is an integer.

 p. 81 #20-40 evens  Yes, there is a lot of writing on this assignment.  If you would prefer to type it, you may do so.