Exercise 3.6 - Equivalence, Entailment, and Consistency

Logical equivalence, logical entailment, and logical consistency are related to each other in interesting ways, but they are not identical. Answer the following true or false questions about the relationships between these concepts.

a.

If φ is equivalent to ψ, then φ entails ψ.

b.

If φ is equivalent to ψ, then φ is consistent with ψ.

c.

If φ entails ψ, then φ is equivalent to ψ.

d.

If φ entails ψ, then φ is consistent with ψ.

e.

If φ is consistent with ψ, then φ is equivalent to ψ.