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) (ii) (iii) The sets A and B are equal. Every element of A is in the set B or the set C. If A is disjoint from B then B and C overlap.
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Solution.
The sets A and B are equal.
Every element of A is in the set B or the set C.
If A is disjoint from B then B and C overlap.