Aim 1.9: To practice writing proofs

Do Now: Given: A v BQ ~ A~ B

Prove: ~ Q

Homework: Packet Page 12 #6Packet Page 13 #42Packet Page 18 #3 CHALLENGETest on Tuesday

**Extra Help After School Thursday, Friday & Monday**

Given:D B~ D P( A ^ B ) C~ CA

Prove: P

Big Proof #1:

Aim 1.9: To practice working with proofs

Statement Reason1. ~ C 1. Given2. ( A ^ B ) C 2. Given3. ~ C ~ ( A^ B ) 3. Contrapositive4. ~ ( A ^ B ) 4. Detachment 1, 35. ~ A v ~ B 5. DeMorgan’s Law6. A 6. Given7. ~ B 7. LODI 5, 68. D B 8. Given9. ~ B ~ D 9. Contrapositive10. ~ D 10. Detachment 7, 911. ~ D P 11. Given12. P 12. Detachment 10, 11

Big Proof #1:

Aim 1.9: To practice working with proofs

Given:~ G F~ ( E ^ F )~ E ~ DA( B ^ C ) DA ( B ^ C )

Prove: G

Big Proof #2:

Aim 1.9: To practice working with proofs

Statement Reason1. A 1. Given2. A ( B ^ C ) 2. Given3. B ^ C 3. Detachment

1, 24. B ^ C D 4. Given5. D 5. Detachment

3, 46. ~ E ~ D 6. Given7. D E 7.

Contrapositive8. E 8. Detachment

5, 7

Big Proof #2:

Aim 1.9: To practice working with proofs

Statement Reason9. ~ ( E ^ F ) 9. Given10. ~ E v ~ F 10. DeMorgan’s

Law11. ~ F 11. LODI 8, 1012. ~ G F 12. Given13. ~ F G 13.

Contrapositive14. G 14.

Detachment 11, 13

Big Proof #2: Continued…

Aim 1.9: To practice working with proofs

Practice: Page 14

Given: Either the Lakers won the game or the Pistons won the game.If Isiah was in the game ad Magic was in the game,

then Kareem was not in the game.If the pistons won the game, then Isiah was in the game.Kareem was in the game.Magic was in the game.

Prove: The Lakers won the game.

L V P

(I ^ M) ~K

P I

K

M

L

Aim 1.9: To practice working with proofs

Page 14 Answer:Statement Reason

1. K 1. Given2. I ^ M ~K 2. Given

3. K ~ (I ^ M ) 3. Contrapositive

4. ~ (I ^ M) 4. Law od Detachment 1, 35. ~ I V ~ M 5. DeMorgan’s Law6. M 6. Given7. ~I 7. LODI 5, 68. P I 8. Given9. ~I ~P 9. Contrapositive

Aim 1.9: To practice working with proofs

Page 14 Answer:Statement Reason

10. ~P 10. Law of Detachment

7, 911. L V P 11. Given

12. L 12. LODI 9, 10

Aim 1.9: To practice working with proofs

Given: A ~ (B ^ C)B v ~GAC

Prove: ~ G

Statement Reason1. A 1. Given2. A ~ ( B ^ C ) 2. Given3. ~ ( B ^ C ) 3. Law of Detachment 1, 24. ~ B v ~ C 4. DeMorgan’s Law5. C 5. Given6. ~ B 6. LODI 4, 57. B v ~ G 7. Given8. ~ G 8. LODI 6, 7

Practice:

Aim 1.9: To practice working with proofs