Properties of Symmetric Difference of Sets

Q. For any two sets $M\&N,\text{if}M\subseteq N,$ then $M△N=$

1. $N-M$
2. $M-N$
3. $\varnothing$

Q. For any two sets $A\&B;n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$, then, $n(A\cap B)=$

Q. For any two sets $A\&B;n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$, then, $n(A\cap B)=$

Q. If $A=\{x:x=2k,k\in N\text{and}k\le 100\}$, $B=\{x:x=2^k,k\in W\text{and}k<11\}$ and $C=\{x:x=k^3,k\in N\text{and}k<11\}$, then the value of $n\left(A△B\right)+n\left(B△C\right)+n\left(A△C\right)$ is

1. $220$
2. $216$
3. $203$
4. $207$

Q. If $n\left(A\right)=50,n\left(B\right)=20,n(A\cap B)=10,$ then $n\left(A\Delta B\right)=$

1. $50$
2. $60$
3. $70$
4. $40$

Q. For any two sets $X\&Y,$
if $X△Y=X,$ then $Y=\varphi .$

1. True
2. False

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. 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. For any two sets $X\&Y$
$X△Y=Y△X.$

1. True
2. False

Q. If $A=\{a,b,c,d\}\text{and}B=\{c,d,e,f\},$ then select the "wrong" statement.

1. $A\Delta B=B\Delta A$
2. $A\Delta B=B-A$
3. $A\Delta B=(A-B)\cap (B-A)$
4. $A\Delta B=A-B$

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 $A=\{x:x^2-9\le 0,x\in Z\}$ and $B=\{x:|x-2|<3,x\in Z\}.$ Then the number of elements in $A\Delta B$ is

1. $3$
2. $4$
3. $5$
4. $6$

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 two sets $X\&Y,$
if $X△Y=X,$ then $Y=\varphi .$

1. True
2. False

Q. For any two sets $A\&B;n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$, then, $n(A\cap B)=$

Q. For any two sets $X\&Y$
$X△Y=Y△X.$

1. True
2. False

Q. For two sets $A\&B$ such that:
$A=\{12,14,15,16,19,20\}$
$B=\{18,21,20,15,17,13\}$
Choose the correct options.

1. $A△B=\{12,14,16,19,18,21,17,13\}$
2. $A△B=\{15,16,20\}$
3. $B△A=\{12,14,16,19,18,21,17,13\}$
4. $B△A=\{15,16,20\}$