1. Aim 1.4: To work with conditionals and biconditionals Do Now: Determine the truth value of the following sentences: 1.9 is a prime number and New York is a state 2.Cars drive on the highway or school is closed 3.Negate: Today is not Wednesday. 4.If today is Tuesday, then we do not have a quiz tomorrow. Homework: Logic Review Sheet Logic Quiz Wednesday Logic Quiz Wednesday

2. Practicing with conditionals Write the converse, inverse and contrapositive of the following sentence: If it is 360 o around, then it is a circle. Converse: If it is a circle, then it is 360 o around. Inverse: If it is not 360 o around, then it is not a circle. Contrapositive: If it is not a circle, then it is not 360 o around. Aim 1.4: To work with conditionals and biconditionals

3. What is the Converse, Inverse and Contrapositive? If today is Friday, then tomorrow is Sunday. Converse: If tomorrow is Sunday, then today is Friday. Inverse: If today is not Friday, then tomorrow is not Sunday. Contrapositive: If tomorrow is not Sunday, then today is not Friday. Aim 1.4: To work with conditionals and biconditionals

4. Review Complete the following truth table: pq~p~q ~p  q ~p V ~q (p V q) ^ ~q TT TF FT FF Aim 1.4: To work with conditionals and biconditionals

5. What is the Converse, Inverse and Contrapositive? If the number is divisible by 2, then it is an even number. Converse: If it is an even number, then the number is divisible by 2. Inverse: If it is not an even number, then it is not divisible by 2. Contrapositive: If it is not an even number, then it is not divisible by 2. Aim 1.4: To work with conditionals and biconditionals

6. What is the Converse, Inverse and Contrapositive? “ If it is a square, then it has four congruent sides. “ Converse: “ If it has four congruent sides, then it is a square. Inverse: “ If it is not a square, then it does not have four congruent sides. Contrapositive: “ If it does not have four congruent sides, then it is not a square. Aim 1.4: To work with conditionals and biconditionals

7. Biconditionals A biconditional joins two facts together using “ if and only if “ A biconditional joins two facts together using “ if and only if “ Example: A triangle is isosceles if and only if it has two congruent sides. Example: A triangle is isosceles if and only if it has two congruent sides. Biconditionals are often used in definitions. Biconditionals are often used in definitions. A biconditional is only true when both facts are either true or false. A biconditional is only true when both facts are either true or false. Aim 1.4: To work with conditionals and biconditionals

8. Biconditionals p and q represent facts. p and q represent facts. pq p  q TTT TFF FTF FFT Aim 1.4: To work with conditionals and biconditionals

9. Examples: 1.A shape is a square if and only if the shape has four congruent sides. ( T ) 2.A number is prime if and only if it is divisible by 2. ( F ) 3.Today is Tuesday if and only if tomorrow is not Thursday ( T ) 4.5 is an even number if and only if 5 is divisible by 0. ( T ) Aim 1.4: To work with conditionals and biconditionals

10. Create two Biconditional statements. Make sure one of the statements is true and one of them is false! Aim 1.4: To work with conditionals and biconditionals

11. Review Questions 1.Find the negation of the sentence: A square has four equal sides. 2.What is the truth value of the statement "2 + 4 = 6 and 9 is a prime number."? 3.The sentence "If _____, then 4 + 3 = 7." is true. Which of the following statements could be used to fill the blank a. 6/3 = 2 b. 8/4 = 3 c. both a and b could be used

12. Review 4.The sentence " _____ if and only if x + x = 3x." is true. Which of the following statements could be used to fill the blank? a. x + x = 2x b. 2x - x = 2x c. both a and b can be used 5.What is the truth value of the statement "If dogs bark, then horses quack."? 6.What is the truth value of the statement 6.What is the truth value of the statement “If it is October, then 8 is a prime number.”

13. Review 7.Determine the truth value of the sentence: “ 7 is an even number or 9 is divisible by 3” 8.If p is true, what is the truth value of ~(~p) ? 9.Which statement will have the same truth value as “If I do not eat lunch, then I will be hungry” a. “If I eat lunch, then I will not be hungry” b. “If I do not eat lunch, then I will not be hungry” c. “If I will not be hungry, then I did eat lunch”

14. Review Write the converse, inverse and contrapositive for the following statement: If a number is divisible by 4, then it is divisible by 2.

15. pq~p~p V q(~p V q)  q TT TF FT FF Practice: Complete the following truth table: Aim 1.4: To work with conditionals and biconditionals