Find the mistake in the following “proof”. “Theorem” for all sets A and B , A c ∪ B c ⊆ ( A ∪ B ) c . “Proof:Suppose A and B are sets, and x ∈ A c ∪ B c by definition of union. It follows that x ∈ A and x ∈ B by definition of complement, and so x ∈ A ∪ B by definiton of union. Thus x ∈ ( A ∪ B ) c by definiton of complement and hence A c ∪ B c ⊆ ( A ∪ B ) c ”.

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Chapter 6.2, Problem 21ES

To determine

Find the mistake in the following “proof”.

“Theorem” for all sets A and B, Ac∪Bc⊆(A∪B)c.

“Proof:Suppose A and B are sets, and x∈Ac∪Bc by definition of union. It follows that x∈A and x∈B by definition of complement, and so x∈A∪B by definiton of union.

Thus x∈(A∪B)c by definiton of complement and hence Ac∪Bc⊆(A∪B)c ”.

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