Subset and Superset

Q. Let $A=\{2,4,6\}$ and $B=\{x:x\text{is an even natural number less than}8\}$, then which of the following is/are correct?

1. $A\subset B$
2. $B\subset A$
3. $A\ne B$
4. $n\left(A\right)<n\left(B\right)$

Q. If $A$ and $B$ are finite sets and $A\subset B,$ then

1. $n(A\cup B)=n\left(A\right)$
2. $n(A\cap B)=n\left(B\right)$
3. $n(A\cup B)=n\left(B\right)$
4. $n(A\cap B)=\varphi$

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 is not true for two non-empty sets A and B?

1. If A $\subseteq$ B and B $\subseteq$ A, then A = B.

2. For every set A, empty set $\varphi$ and A itself, are the subsets.

3. If A $\subset$ B and A $\ne$B, then B is called superset of A.

4. If A $\subset$ B and A $\ne$B, then A is called superset of B.

Q.

Which of the following is not true for two non-empty sets A and B?

1. If A $\subseteq$ B and B $\subseteq$ A, then A = B.

2. For every set A, empty set $\varphi$ and A itself, are the subsets.

3. If A $\subset$ B and A $\ne$B, then B is called superset of A.

4. If A $\subset$ B and A $\ne$B, then A is called superset of B.

Q. If the solution set of $|x-k|<2$ is a subset of the solution set of the inequality $\frac{2x-1}{x+2}<1,$ then the number of possible integral value(s) of $k$ is

1. $0$
2. $1$
3. $2$
4. $3$

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

1. False
2. True

Q. For a given pair of sets, identify the pair where the first set is the subset of the second set.

1. $\{p,q,r\}\&\{a,p,b,q,c,r\}$
2. $\{x:x\text{is an isoceles triangle in}x-y\text{plane}\}\&$ $\{y:y\text{is a triangle in}x-y\text{plane}\}$
3. $\{m:m\text{is a multiple of 10}\}\&$ $\{n:n\text{is a multiple of 5}\}$
4. $\{b:b\text{is a vowel in the word TEA}\}\&$ $\{c:c\text{is a vowel in the word CAT}\}$

Q. If $A\subset B,$ then which of the following is not true?

1. $A\cup B=B$
2. $A\cap B=B$
3. $A\cap B=A$
4. $A-B=\Phi$

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