Let A, B, C be subsets of a set X. Which of t | vedclass

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(B) We evaluate the expression $(A \setminus B) \setminus C$: By definition of set difference,$A \setminus B = A \cap B'$. Thus,$(A \setminus B) \setm

Vedclass · Accepted Answer

$(A \setminus B) \setminus C = A \setminus (B \cup C)$

Vedclass · Answer

(B) We evaluate the expression $(A \setminus B) \setminus C$: By definition of set difference,$A \setminus B = A \cap B'$. Thus,$(A \setminus B) \setminus C = (A \cap B') \cap C'$. Using the associative property of intersection,we get $A \cap (B' \cap C')$. By De Morgan's Law,$B' \cap C' = (B \cup C)'$. Therefore,$(A \setminus B) \setminus C = A \cap (B \cup C)' = A \setminus (B \cup C)$. Hence,the statement in option $B$ is valid.

Let $A, B, C$ be subsets of a set $X$. Which of the following set-theoretic statements is valid?

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