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Aim 1.9: To practice writing proofs

Aim 1.9: To practice writing proofs. Do Now: Given: A v B Q  ~ A ~ B Prove: ~ Q Homework: Packet Page 12 #6 Packet Page 13 #42 Packet Page 18 #3 CHALLENGE Test on Tuesday **Extra Help After School Thursday, Friday & Monday**. Big Proof #1:. Given: D  B ~ D  P

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Aim 1.9: To practice writing proofs

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  1. Aim 1.9: To practice writing proofs Do Now: Given: A v B Q  ~ A ~ B Prove: ~ Q Homework: Packet Page 12 #6 Packet Page 13 #42 Packet Page 18 #3 CHALLENGE Test on Tuesday **Extra Help After School Thursday, Friday & Monday**

  2. Big Proof #1: Given: D  B ~ D  P ( A ^ B )  C ~ C A Prove: P Aim 1.9: To practice working with proofs

  3. Big Proof #1: Statement Reason 1. ~ C 1. Given 2. ( A ^ B )  C 2. Given 3. ~ C  ~ ( A^ B ) 3. Contrapositive 4. ~ ( A ^ B ) 4. Detachment 1, 3 5. ~ A v ~ B 5. DeMorgan’s Law 6. A 6. Given 7. ~ B 7. LODI 5, 6 8. D  B 8. Given 9. ~ B  ~ D 9. Contrapositive 10. ~ D 10. Detachment 7, 9 11. ~ D  P 11. Given 12. P 12. Detachment 10, 11 Aim 1.9: To practice working with proofs

  4. Big Proof #2: Given: ~ G  F ~ ( E ^ F ) ~ E  ~ D A ( B ^ C )  D A  ( B ^ C ) Prove: G Aim 1.9: To practice working with proofs

  5. Big Proof #2: Statement Reason 1. A 1. Given 2. A  ( B ^ C ) 2. Given 3. B ^ C 3. Detachment 1, 2 4. B ^ C  D 4. Given 5. D 5. Detachment 3, 4 6. ~ E  ~ D 6. Given 7. D  E 7. Contrapositive 8. E 8. Detachment 5, 7 Aim 1.9: To practice working with proofs

  6. Big Proof #2: Continued… Statement Reason 9. ~ ( E ^ F ) 9. Given 10. ~ E v ~ F 10. DeMorgan’s Law 11. ~ F 11. LODI 8, 10 12. ~ G  F 12. Given 13. ~ F  G 13. Contrapositive 14. G 14. Detachment 11, 13 Aim 1.9: To practice working with proofs

  7. 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. Practice: Page 14 L V P (I ^ M)  ~K P  I K M L Aim 1.9: To practice working with proofs

  8. Page 14 Answer: Statement Reason 1. K 1. Given 2. I ^ M  ~K 2. Given 3. K  ~ (I ^ M ) 3. Contrapositive 4. ~ (I ^ M) 4. Law od Detachment 1, 3 5. ~ I V ~ M 5. DeMorgan’s Law 6. M 6. Given 7. ~I 7. LODI 5, 6 8. P  I 8. Given 9. ~I  ~P 9. Contrapositive Aim 1.9: To practice working with proofs

  9. Page 14 Answer: Statement Reason 10. ~P 10. Law of Detachment 7, 9 11. L V P 11. Given 12. L 12. LODI 9, 10 Aim 1.9: To practice working with proofs

  10. Practice: Given: A  ~ (B ^ C) B v ~G A C Prove: ~ G Statement Reason • A 1. Given • A  ~ ( B ^ C ) 2. Given • ~ ( B ^ C ) 3. Law of Detachment 1, 2 • ~ B v ~ C 4. DeMorgan’s Law • C 5. Given • ~ B 6. LODI 4, 5 • B v ~ G 7. Given • ~ G 8. LODI 6, 7 Aim 1.9: To practice working with proofs

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