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

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(D) Let us analyze each relation:$(1) \, A - B = A - (A \cap B)$: This is a standard set identity. The set $A - B$ consists of elements in $A$ that ar

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$1$ and $2$

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(D) Let us analyze each relation:$(1) \, A - B = A - (A \cap B)$: This is a standard set identity. The set $A - B$ consists of elements in $A$ that are not in $B$. Since $A \cap B$ is the set of elements common to both $A$ and $B$,removing these from $A$ leaves exactly $A - B$. Thus,$(1)$ is correct.$(2) \, A = (A \cap B) \cup (A - B)$: This represents the partition of set $A$ into two disjoint sets: the part common to $B$ $(A \cap B)$ and the part not in $B$ $(A - B)$. Their union is indeed $A$. Thus,$(2)$ is correct.$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$: According to De Morgan's laws for set difference,$A - (B \cup C) = (A - B) \cap (A - C)$. Therefore,the given relation is incorrect.Conclusion: Relations $(1)$ 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?