Law of Modus Tollens and Invalid Arguments · Law of Modus Tollens and Invalid Arguments SWBAT: Use...
Transcript of Law of Modus Tollens and Invalid Arguments · Law of Modus Tollens and Invalid Arguments SWBAT: Use...
Warm – Up
Write a formal proof to show that the conclusion must follow from the given set of premises.
Given: If two lines intersect, the lines meet at only one point. Lines k and m do not meet at one point. Prove: Lines k and m do not intersect
SWBAT: Use the Law of Modus Tollens in formal proofs
Given: I P P Prove: I
SWBAT: Use the Law of Modus Tollens in formal proofs
Given: I P P Prove: I
Statements Reasons
1) I P 1) Given
2) P I 2) Law of Contrapositive (1)
3) P 3) Given
4) I 4) Law of Detachment (2, 3)
Law of contrapositive
Law of detachment
and
SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.
SWBAT: Use the Law of Modus Tollens in formal proofs
Statements Reasons
1. R Q 1. Given
2. R 2. Given
3. Q 3. Law of Detachment (1, 2) 4. S Q 4. Given
5. S 5. Law of Modus Tollens (4, 3) Think: Q S
SWBAT: Use the Law of Modus Tollens in formal proofs
Statements Reasons
1. R Q 1. Given
2. R 2. Given
3. Q 3. Law of Detachment (1, 2)
4. S Q 4. Given
5. Q S
5. Law of Contrapositive (4)
6. S 6. Law of Detachment (5, 3)
SWBAT: Use the Law of Modus Tollens in formal proofs
Given: w b b Prove: w
Statements Reasons
1) w b 1) Given
2) b 2) Given
3) w 3) Law of Modus Tollens (4, 3)
Think: b w
SWBAT: Use the Law of Modus Tollens in formal proofs
Given: w b b Prove: w
Statements Reasons
1) w b 1) Given
2) b w 2) Law of Contrapositive (1)
3) b 3) Given
4) w 4) Law of Detachment (2, 3)
SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.
[(p→q)q] → p [(p→q)q]
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[(p→q)q] → p
[(p→q)q] → p Is an invalid argument because it is not a tautology.