Solution to Consider the following assertions about the sets A, B and C. Write them down in … - Sikademy
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Archangel Macsika

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.

\forall x (x\isin A\implies x \in B) \land (x \in B \implies x \in A).

Every element of A is in the set B or the set C.

\forall x (x \in A )\implies (x\in B \lor x \in C).

If A is disjoint from B then B and C overlap.

\forall x ((x \in A \land x \notin B)\lor (x \in B \land x \notin A)\implies (x \in B \land x\in C).

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