CONDITIONAL STATEMENTS Logic Lesson 1 Conditional Statement Negation

CONDITIONAL STATEMENTS Logic Lesson 1

Conditional Statement Negation Equivalent Statements Converse Inverse Contrapositive CONDITIONAL STATEMENTS FOLDABLE

CONDITIONAL STATEMENT if-then false true If you are from Wisconsin, then you are a Packer fan! hypothesis conclusion

CONVERSE flipping AB+BC=AC B is between A & C

NEGATION It is not raining I am hungry opposite

INVERSE Inverse = Opposite negating If you are NOT from Wisconsin, then you are NOT a Packer fan! If you are from Wisconsin, then you are a Packer fan! An angle is not 90 It is not a right angle

CONTRAPOSITIVE flipping negating If you are from Wisconsin, then you are a Packer fan! two angles are not ≅ they are not vertical angles If you are NOT a Packer fan, then you are NOT from Wisconsin!

EQUIVALENT STATEMENTS contrapositive converse inverse If you are from Wisconsin, then you are a Packer fan! I am from Wisconsin, therefore I must be a Packer fan. true false If you are NOT a Packer fan, then you are NOT from Wisconsin! I am NOT a Packer fan, therefore I must NOT be from Wisconsin.

CONDITIONAL STATEMENTS NOTES If you graduate high school, then you go to college. If hypothesis, then conclusion. Converse (Flip) If you go to college, then you graduated high school. Inverse (Negate) If you did not graduate high school, then you did not go to college. Contrapositive (Flip and Negate) If you did not go to college, then you did not graduate high school.

CONDITIONAL STATEMENTS NOTES If you get married, then you have three children. You can provide a counterexample to prove statements are false. Converse (Flip) If you have three children, then you got married. Inverse (Negate) If you do not get married, then you do not have three children. Contrapositive (Flip and Negate) If you do not have three children, then you did not get married.

If a conditional statement is true then: TRUE the converse is. SOMETIMES _________ TRUE the inverse is. SOMETIMES __________ TRUE the contrapositive is. ALWAYS ________ CONDITIONAL STATEMENT NOTES

Identify the hypothesis and conclusion. You will make the honor roll if you get all A’s and B’s. CLASS EXAMPLE 1

Provide a counterexample to show that the conditional statement is false. If a number is odd, then it is a prime number. CLASS EXAMPLE 2

Write the inverse of the statement. Is it true or false? If false provide a counterexample. If a bird is a raven then it is black. CLASS EXAMPLE 3

Write the converse of the statement. AB = BC if B is the midpoint of AC. STUDENT EXAMPLE 1

Identify the hypothesis and conclusion. If you build it they will come. STUDENT EXAMPLE 2

Write the inverse. Is it true? If not, provide a counterexample. ∠A=∠B if both angles are right angles. STUDENT EXAMPLE 3