Consider the following relations:(1) , A - B | vedclass

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(D) For $(1)$: $A - B$ is the set of elements in $A$ but not in $B$. $A \cap B$ is the set of elements common to $A$ and $B$. Thus,$A - (A \cap B)$ al

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$1$ and $2$

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(D) For $(1)$: $A - B$ is the set of elements in $A$ but not in $B$. $A \cap B$ is the set of elements common to $A$ and $B$. Thus,$A - (A \cap B)$ also represents elements in $A$ that are not in $B$. So,$(1)$ is correct.For $(2)$: The set $A$ can be partitioned into two disjoint sets: elements in $A$ that are also in $B$ $(A \cap B)$ and elements in $A$ that are not in $B$ $(A - B)$. Their union is $A$. So,$(2)$ is correct.For $(3)$: By De Morgan's Law,$A - (B \cup C) = A \cap (B \cup C)^c = A \cap (B^c \cap C^c) = (A \cap B^c) \cap (A \cap C^c) = (A - B) \cap (A - C)$. The given relation uses $\cup$ instead of $\cap$. So,$(3)$ is incorrect.Therefore,$(1)$ and $(2)$ are correct.

Consider the following relations:
$(1) \, A - B = A - (A \cap B)$
$(2) \, A = (A \cap B) \cup (A - B)$
$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$
Which of these is/are correct?

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Consider the following relations:$(1) \, A - B = A - (A \cap B)$$(2) \, A = (A \cap B) \cup (A - B)$$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$Which of these is/are correct?