Conditional Statements (aka if-then statements)
  Written in the form if A, then B
  hypothesis: A   conclusion: B

Example 1: Identify the hypothesis and conclusion of each statement
  A) If it is raining, then Beau and Chloe will not play softball.
   Hypothesis:

   Conclusion:



  B) If 7y + 5 ≤ 26, then y ≤ 3
   Hypothesis:

   Conclusion:





The hypothesis is the part the follows the word "if" and the conclusion is the part following the word "then." The hypothesis always has to happen first. The conclusion follows as a result of it.

Example 2: Identify the hypothesis and conclusion of each statement. Then write each in if-then form.
*These examples are more difficult, there is not word if or then. So think about what has to happen first, and then what you can conclude about the event because it took place. Thats how you can answer these questions
  A) I eat light meals
   Hypothesis:

   Conclusion:

   If-Then Form:

  B) For a number a such that 8 + 5a = 43, then a = 7
   Hypothesis:

   Conclusion:

   If-Then Form:

Deductive Reasoning: Process of using facts, rules, definitions or properties to reach a valid conclusion.

Example 3: Statement: If one number is odd, and another number is even, then their sum is odd.
Determine a valid conclusion based upon the statement. If no valid conclusion exists, write "no valid conclusion" and explain why.
  A) The numbers are 5 and 12




  B) The numbers are 8 and 26

Counterexample: specific case in which a statement is false

To show something true: need a proof
To show something false: need a counterexample

Example 4: Provide a counterexample for each conditional statement.
  A) If Joe did not eat lunch, then he must not feel well.




  B) If the traffic light is red, then the cars must be stopped.

Homework: p39 #2, 18-41, 59, 68, 72