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Find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U = {1, 2, 3, 4, 5}. (Enter your answers for A, B, and C in roster notation as a comma-separated list of sets. Enter EMPTY or ∅ for the empty set.) For all sets A, B, and C,

AU (B-C) = (AUB) - (AUC).
A, B, C = ____.

Respuesta :

Answer:

A = {1}

B = {2}

C = empty set

Step-by-step explanation:

REcall that given sets A, B then A-B = [tex]A \cap B^c[/tex], recall also that the complement of the empty set is the universe set U.

Then,

[tex] A \cup (B-C) = A\cup (B\cap \emptyset^c) = A\cup (B) = A \cup B = \{1,2\}[/tex]

Also, recall that given a set A, the union of A with the empty set is again the set A. Then

[tex] (A \cup B) - (A\cup \emptyset) = (A\cup B)- A = B-A =\{2\}-\{1\} = \{2\}[/tex]

But, [tex]\{1,2\} \neq \{2\}[/tex]

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