Introduction to Logic - Exercise 3.4

Introduction to Logic

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Exercise 3.4 - Propositional Entailment

Let Γ and Δ be sets of sentences in Propositional Logic, and let φ and ψ be individual sentences in Propositional Logic. State whether each of the following statements is true or false.

a.	If Γ ⊨ φ and Δ ⊨ φ, then Γ ∩ Δ ⊨ φ.
b.	If Γ ⊨ φ and Δ ⊨ φ, then Γ ∪ Δ ⊨ φ.
c.	If Γ ⊨ φ and Δ ⊭ φ, then Γ ∪ Δ ⊨ φ.
d.	If Γ ⊭ ψ, then Γ ⊨ ¬ψ.
e.	If Γ ⊨ ¬ψ, then Γ ⊭ ψ.