Mathematical Thinking Stanford, W2 Assignment 3
1. D, Y, T
a. T ⇒ [D ∧ Y]
b. D ⇒ ¬ Y
c. ¬ D ⇒ ¬ T
d. T ⇒ ¬ (D ∧ Y)
e. ¬ D ∧ Y ∧ T , T ⇒ [¬ D ∧ Y], following means “then or and”, they are all conjunctions relationship.
f. (T ∧ Y) ⇒ ¬ D , T ⇒ [Y ⇒ ¬ D]
g. T ⇒ [D ⇔ Y], T⇒ [(D ⇒Y) ∧ (Y⇒D)]
h. T ⇒ (¬D ∧ Y) ∨ (D ∧ ¬Y)
2. Truth table
| φ | ¬φ | ψ | ||
|---|---|---|---|---|
| φ⇒ψ | ¬φ∨ψ | |||
| T | F | T | T | T |
| T | F | F | F | F |
| F | T | T | T | T |
| F | T | F | T | T |
3 Conclusions of above table
φ⇒ψ = ¬φ∨ψ
4 truth table
| φ | ψ | ¬φ | φ⇒ψ | φ̸⇏ψ | φ∧¬ψ |
|---|---|---|---|---|---|
| T | T | F | T | F | F |
| T | F | F | F | T | T |
| F | T | T | T | F | F |
| F | F | T | T | F | F |
5 Conclusions of above table
φ̸⇏ψ = φ∧¬ψ
Woman swerves and sleeping dogs
V = Views Dog
S = Swerves
| V | S | V⇒S |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |