Baby Logic Practice: Derive the Conclusions

Difficulty: What the hell

Today’s post is simple: a few symbolic-logic proof exercises. No quantifiers. No modal logic. Just derive the indicated conclusions from the premises supplied. These are not one-step gimmies, so slow down and actually work through them.

I’ll likely post solutions tomorrow.

Exercise 1

1. P → Q

2. Q → R

3. P ∨ S

4. ¬R

∴ S

Exercise 2

1. P → (Q ∧ R)

2. ¬R ∨ S

3. P

∴ S

Exercise 3

1. P → Q

2. R → S

3. ¬Q

4. P ∨ R

∴ S

Exercise 4

1. (P ∨ Q) → R

2. ¬R

∴ ¬P ∧ ¬Q

Exercise 5

1. P → Q

2. Q → (R ∨ S)

3. ¬R

4. P

∴ S

Exercise 6

1. P ↔ Q

2. Q → R

3. ¬R

∴ ¬P

Exercise 7

1. (P ∧ Q) → R

2. P

3. ¬R

∴ ¬Q

Exercise 8

1. P → Q

2. Q → R

3. R → S

4. ¬S

∴ ¬P

If these still feel too easy, good. Basic logical competence should eventually feel boringly obvious. That’s the point.