Question

Explain the relationship between logical equivalences and set identities.

Short answer

Each logical; equivalence corresponds with a set identity which is obtained by replacing $\wedge$by $\cap$, $\wedge$by $\cup$, T by$\cup$ (universal set), F by$\varnothing$ (empty set) and $\neg$by ${}^{-}$.

Step-by-step solution

Definitions

Union$A\cup B$ represents all elements that are either in A or in B.

Intersection $A\cap B$represents all elements that are both in A and in B.

Difference A-B represents all elements in A that are not in B.

Logical equivalence

Each logical equivalence corresponds with a set identity which is obtained by replacing $\wedge$by $\cap$, $\vee$by $\cup$, T by $\cup$(universal set), F by $\varnothing$(empty set) and $\neg$by -.

Moreover, the name of a logical equivalence tends the same as the name of the corresponding set identity.