Discrete Math: Find the mistake(s) in the following \"proof\" Find the mistake(s

Question

Discrete Math:

Find the mistake(s) in the following "proof"

Find the mistake(s) in the following "proof" Theorem: For all sets A and B A' Union B' subset (A Union B)' Proof: S ' pose A, Bare sets with x elementof A Union B. Then x Elementof A or X Elementof B by definition of union. It follows that x notequalto A or x elementof B, by definition of complement and so x notequalto A Union B by definition of union. Thus x elementof A Union B by definition of complement, and hence A' union B' subset (A union B)'

Explanation / Answer

Given that, x A'B' and in the proof it is mention that "xA' or xB' by definition of union".

Let us assume that this line is true.

Now assume x only belongs to A' according to the above line.

Then x can not belongs to AB' because xA', and hence A'B' can not be the subset of (AB)'.

Therefore "xA' or xB' by definition of union" this line contradicts our proof.

So we replace this line by "xA' or xB' or both by definition of union" for a correct proof.

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