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. $2$. $A - (A \cap B) = A \cap (A \cap B)' = A \cap (A' \cup B') = (A \cap A') \cup (A \cap B') = \emptyset \cup (A \cap B') = A \cap B'$. Thus,$A - B = A - (A \cap B)$ is true. $3$. $(A \cup B) - B = (A \cup B) \cap B' = (A \cap B') \cup (B \cap B') = (A \cap B') \cup \emptyset = A \cap B'$. Thus,$A - B = (A \cup B) - B$ is true. $4$. $A - B'$ is the set of elements in $A$ that are not in $B'$,which means elements in $A$ that are in $B$. Thus,$A - B' = A \cap B$. Since $A \cap B 
eq A \cap B'$ in general,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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