1. Equivalent Statements and Variations of Conditional Statements
13.5 Notes
Equivalent Statements and Variations of Conditional Statements
* 2 class work slides to be done on a separate sheet of paper with a partner

2. Warm-up
Use a truth table to show that p and ~(~p) are equivalent statements.

3. Equivalent Statements
p: I attend class q: I fail the course Using a truth table show that and are equivalent. p q
p or q ~q
~qp

4. Class Work: Equivalent Statements
Show is equivalent to ~p ~q p q ~q ~p
p or not q
~p ~q

5. Contrapositive
The contrapositive of a conditional statement is a statement obtained by reversing and negating the antecedent (if part) and the consequent (then part).
p  q is EQUIVALENT to it’s contrapositive
Write an equivalent contrapositive for the following statement:
If you live in Los Angeles, then you live in California

6. Converse and Inverse For the conditional statement p q
Converse: antecedent and consequent are reversed
Symbolic:
Inverse: antecedent and consequent are negated.
Write the converse and inverse for the following statement:
If it’s a BMW, then it’s a car.

7. Classwork: Complete the table
Variations
Symbolic Statement
English Translation
Given conditional statement
p q
If you are 17, then you are not eligible to vote
Converse
Inverse
Contrapositive