Consider the following assertions about the sets A, B and C. Write them down in the language of predicate logic. Use only the constructions of predicate logic (∀, ∃, ¬, ⇒, ∧, ∨) and the element- of...

Consider the following assertions about the sets A, B and C. Write them down in the language of

predicate logic. Use only the constructions of predicate logic (∀, ∃, ¬, ⇒, ∧, ∨) and the element-
of symbol (∈). Do not use derived notions (∩, ∪, =, etc.).

Hint “A is a subset of B” can be formalized as ∀x. x ∈ A =⇒ x ∈ B.

(i) The sets A and B are equal.
(ii) Every element of A is in the set B or the set C.

(iii) If A is disjoint from B then B and C overlap.