If A B = B, then B A? If A and B are disjoint sets, then n(A B) = n(A) + n(B)? For any two sets A and B, n(A) + n(B) - n(A B) = n(A B)?

The question states: "যদি $A \cap B = B$ হয়, তবে—" (If $A \cap B = B$, then—).
If the intersection of set $A$ and set $B$ is equal to set $B$, it means that all elements of $B$ are also elements of $A$. This is the definition of $B$ being a subset of $A$.

Therefore, $B \subseteq A$.

The correct option is B.
$\boxed{\text{B}}$

The question states: "$A$ ও $B$ দুটি বিচ্ছেদ (disjoint) সেট হলে, $n(A \cup B) =$" (If $A$ and $B$ are two disjoint sets, then $n(A \cup B) =$).
For any two finite sets $A$ and $B$, the number of elements in their union is given by the formula:

$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$

If $A$ and $B$ are disjoint sets, it means they have no common elements. Therefore, their intersection is the empty set, $A \cap B = \phi$, and the number of elements in their intersection is $n(A \cap B) = 0$.
Substituting $n(A \cap B) = 0$ into the formula:

$$n(A \cup B) = n(A) + n(B) - 0$$ $$n(A \cup B) = n(A) + n(B)$$

The correct option is A.
$\boxed{\text{A}}$

The question states: "যে-কোনো দুটি সেট $A$ ও $B$-এর ক্ষেত্রে, $n(A) + n(B) - n(A \cap B) =$" (For any two sets $A$ and $B$, $n(A) + n(B) - n(A \cap B) =$).
This is the fundamental formula for the number of elements in the union of two finite sets.

$$n(A) + n(B) - n(A \cap B) = n(A \cup B)$$

The correct option is A.
$\boxed{\text{A}}$

The question states: "$A \cup U = U$-এর দ্বৈত অভেদ হবে—" (The dual identity of $A \cup U = U$ will be—).
To find the dual of a set identity, we interchange the union operator ($\cup$) with the intersection operator ($\cap$), and the universal set ($U$) with the empty set ($\phi$).
Given identity: $A \cup U = U$

1. Replace $\cup$ with $\cap$: $A \cap U$
2. Replace $U$ with $\phi$: $A \cap \phi$
3. Replace $U$ with $\phi$ on the right side: $\phi$ So, the dual identity is $A \cap \phi = \phi$.

The correct option is D.
$\boxed{\text{D}}$

The question states: "$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ অভেদের দ্বৈত অভেদ হয়—" (The dual identity of $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ is—).
To find the dual of a set identity, we interchange the union operator ($\cup$) with the intersection operator ($\cap$), and vice versa.
Given identity: $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

1. Replace $\cup$ with $\cap$: $A \cap (\dots)$ and $(\dots) \cap (\dots)$
2. Replace $\cap$ with $\cup$: $(\dots B \cup C \dots)$ and $(\dots A \cup B \dots)$ and $(\dots A \cup C \dots)$ Applying these changes to the given identity: Left side: $A \cup (B \cap C)$ becomes $A \cap (B \cup C)$ Right side: $(A \cup B) \cap (A \cup C)$ becomes $(A \cap B) \cup (A \cap C)$ So, the dual identity is $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$. This is the distributive law of intersection over union.

The correct option is A.
$\boxed{\text{A}}$