Law of Modus Tollens and

Invalid Arguments SWBAT:

Use the Law of Modus Tollens in formal proofs

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)

SWBAT: Use the Law of Modus Tollens in formal proofs

Law of contrapositive

Law of detachment

and

SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.

I am not smart

SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.

Think: c s

SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.

Think: q r

SWBAT: Use the Law of Modus Tollens 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 in formal proofs

SWBAT: Use the Law of Modus Tollens and Chain Rule in formal proofs.

[(p→q)q] → p [(p→q)q]

T

F

T

T

T

F

T

F

T

T

F

T

[(p→q)q] → p

[(p→q)q] → p Is an invalid argument because it is not a tautology.

SWBAT: Use the Law of Modus Tollens in formal proofs

SWBAT: Use the Law of Modus Tollens in formal proofs

SWBAT: Use the Law of Modus Tollens in formal proofs

SWBAT: Use the Law of Modus Tollens in formal proofs

SWBAT: Use the Law of Modus Tollens in formal proofs