It is only necessary to prove that other relationships can be expressed with and without.

Or it can be expressed by negation:

A ∨ B = (A' ∧ B ')'

For the convenience of typing, use a' to indicate the right or wrong of a.

Imply can be expressed with and without:

A → B = A' ∨ B = (A ∧ B ')'

Equivalent energy and non-representativeness:

A is equivalent to b = (a → b) ∧ (b→ a) = (a → b')' ∧ (b → a')'

That's basically it.