Consider the following statements:

(a) False ⊨ True

(b) If α ⊨ (β ∧ γ) then α ⊨ β and α ⊨ γ. Which of the following is correct?

1. ABoth statement (a) and statement (b) are false.
2. BStatement (a) is true but statement (b) is false.
3. CStatement (a) is false but statement (b) is true.
4. DBoth statement (a) and statement (b) are true.

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: D. Both statement (a) and statement (b) are true.

Explanation

False has no models, so it entails everything (a true). Every model of α makes β ∧ γ true, hence both β and γ (b true).