Properties of Symmetric Difference of Sets

Q.

If $A$ and $B$ are two sets then $(A-B)\cup (B-A)\cap (A\cap B)$ is equal to

1. $A\cup B$

2. $A\cap B$

3. $A$

4. $B$

Q.

If $A$ and $B$ are two sets then $(A-B)\cup (B-A)\cap (A\cap B)$ is equal to

1. Only $A$

2. $A\cup B$

3. $(A\cup B)$

4. None of these

Q. Let $A=\{x:x\in N\text{and}{x}^2-2x-35<0\}$ and $B=\{x:x\in Z\text{and}1<x+2<10\}.$ Then $n\left(A\Delta B\right)$ is

1. $1$
2. $2$
3. $8$
4. $7$

Q. For any sets $A\&B,A\cup (B-A)=$

1. $A\cap B$
2. $A\cup B$
3. $\varnothing$
4. $A^{\prime }\cap B$

Q. If $A=\{x:x=4k+1,k\in W\text{and}k\le 12\}$ and $B=\{x:x=5^k,k\in W\text{and}k\le 6\}$, then $n\left(A\Delta B\right)$ is

1. $17$
2. $14$
3. $20$
4. $11$

Q. Let $P=\{x:x\in N\text{and}\frac{7}{x+2}>1\}$ and $Q=\{x:x\in N\text{and}|x-1|<2\}.$ Then $n\left(P\Delta Q\right)$ is

1. $7$
2. $8$
3. $2$
4. $4$