Subset and Superset

Q. Two sets $A$ and $B$ are as under :
$A=\left\{\right(a,b)\in R\times R:|a-5|<1\text{and}|b-5|<1\};$
$B=\left\{\right(a,b)\in R\times R:4(a-6{)}^2+9(b-5{)}^2\le 36\}.$ Then

1. neither $A\subset B$ nor $B\subset A$
2. $B\subset A$
3. $A\subset B$
4. $A\cap B=\varphi$ (an empty set)

Q. If a set $A$ is a subset of another set $B,$ then $B$ is a superset of $A.$

1. False
2. True

Q. Which of the following sets are the subsets of $A=\{k:k\text{is a factor of}48\}?$

1. $\{1,2,4,8\}$
2. $\{1,12,16,24,48\}$
3. $\{1,48\}$
4. $\{1,2,3,4,6,8,12,24,48\}$

Q. Every set is a subset of itself.

1. True
2. False

Q. Let $A,B$ and $C$ be sets such that $\varphi \ne A\cap B\subseteq C$. Then which of the following statements is not true ?

1. $B\cap C\ne \varphi$
2. $(C\cup A)\cap (C\cup B)=C$
3. If $(A-B)\subseteq C,$ then $A\subseteq C$
4. If $(A-C)\subseteq B,$ then $A\subseteq B$

Q. If $X=8^n-7n-1,n\in NandY=49(n-1),n\in N$, then -

1. X ⊆ Y
2. Y ⊆ X
3. X = Y
4. None of these

Q. If $X=\{8^n-7n-1|n\in N\}$ and $Y=\left\{49\right(n-1)|n\in N\},$ then

1. $Y\subset X$
2. $X=Y$
3. $X\subset ̸Y$
4. $X\subset Y$

Q. Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A\times B$ having $3$ or more elements is :

1. $256$
2. $220$
3. $219$
4. $211$

Q. An Empty Set $\left(\varnothing \right)$ is a subset of every set.

1. False
2. True

Q. If a set $A$ is not a subset of another set $B,\Rightarrow A\subset ̸B.$

1. False
2. True