1. 1.7 Logical Reasoning and Counterexamples
Conditional Statements (If – then statements)
If there is math class, then there is homework.
Hypothesis
Conclusion

2. Example #1: Identify the hypothesis and conclusion of each statement.
A) If it is raining, then Beau and Chloe will not play softball.
B) If 7y + 5 < 26, then y < 3.
A) If it is raining, then Beau and Chloe will not play softball.
B) If 7y + 5 < 26, then y < 3.

3. Check Your Progress with #1 A & B
A) If it is warm this afternoon, then we will have the party outside.
B) If 8w – 5 = 11, then w = 2.

4. A) I will go to the ball game with you on Saturday.
Example #2: Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.
A) I will go to the ball game with you on Saturday.
B) For a number x such that 6x – 8 = 16, x = 4
If it’s Saturday, then I will go to the ball game.
If 6x – 8 = 16, then x = 4.

5. Deductive Reasoning: Reaching a valid conclusion based on facts, rules, definitions, or properties
Example #3: Determine a valid conclusion that follows from the statement, “if two numbers are odd, then their sum is even” for the given conditions. If a valid conclusion does not follow, write no valid conclusion and explain why.
A) the two numbers are 7 and 3
B) the sum of two numbers is 14
A) 7 & 3 are odd, so the hypothesis is true. There is a valid conclusion.
B) The conclusion is true. But if the numbers were 8 & 6, then the hypothesis is false. There is no valid conclusion.

6. Counterexample: A specific case where the statement is false
You only need 1 counterexample to prove a statement false.
Provide a counterexample for each conditional statement.
A) If Joe did not each lunch, then he must not feel well.
B) If the traffic light is red, then the cars must be stopped.
Maybe Joe just didn’t have time.
Maybe a policeman is there to direct traffic.

7. Homework Assignment #6
p even, 47-49