Which of the following statements is false (w | vedclass

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(C) The set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$.$1$. $A - B = A \cap B'$ is a standard identity.$2$. $

Vedclass · Accepted Answer

$A - B = A - B'$

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(C) The set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$.$1$. $A - B = A \cap B'$ is a standard identity.$2$. $A - (A \cap B) = A \cap (A \cap B)' = A \cap (A' \cup B') = (A \cap A') \cup (A \cap B') = \emptyset \cup (A \cap B') = A \cap B'$,which is equal to $A - B$.$3$. $(A \cup B) - B = (A \cup B) \cap B' = (A \cap B') \cup (B \cap B') = (A \cap B') \cup \emptyset = A \cap B'$,which is equal to $A - B$.$4$. $A - B'$ is equal to $A \cap (B')' = A \cap B$,which is generally not equal to $A - B$ unless $A \cap B = \emptyset$.Therefore,the statement $A - B = A - B'$ is false.

Which of the following statements is false (where $A$ and $B$ are two non-empty sets)?

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