Subset and Superset

Q. Every set is a subset of itself.

1. True
2. False

Q. Let $P,Q,R,S$ be the four sets such that $P=\{3,5,7,9,11\},Q=\{9,11,13\},$ $R=\{3,5,9\}$ and $S=\{13,11\}$. Which of the following options is/are correct?

1. $R\subset P$
2. $Q\subset P$
3. $R\subset S$
4. $S\subset Q$

Q.

If $p,q,r$ are any three logical statements, then which one of the following is correct?

1. $~[p\wedge (~q\left)\right]\equiv (~p)\wedge q$

2. $~(p\vee q)\wedge (~r)\equiv (~p)\vee (~q)\vee (~r)$

3. $~[p\vee (~q\left)\right]\equiv (~p)\wedge q$

4. $~[p\wedge (~q\left)\right]\equiv (~p)\wedge ~q$

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

1. False
2. True

Q. Let $S=\{1,2,3,4,5,6,9\}$. Then the number of elements in the set $T=\{A\subseteq S:A\ne \varphi$ and the sum of all the elements of $A$ is not a multiple of $3\}$ is

Q. Let $S=\{1,2,3,4,5,6,9\}$. Then the number of elements in the set $T=\{A\subseteq S:A\ne \varphi$ and the sum of all the elements of $A$ is not a multiple of $3\}$ is

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

1. False
2. True

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

1. False
2. True

Q. If $U=\{1,3,5,7,9,11,13\}$, then which of the following is/are the subsets of $U$?

1. $A=\left\{0\right\}$
2. $B=\{1,9,5,13\}$
3. $C=\{3,11,7\}$
4. $D=\{2,3,4,5\}$

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

1. $A\subseteq B$
2. $B\supseteq A$
3. $\mathrm{if}a\in A\Rightarrow a\in B$
4. $\mathrm{if}a\in B\Rightarrow a\in A$

Q. Which of the following is a superset of the set $X=\{k:k\text{is a factor of}6\}?$

1. $M=\{m:m\text{is a factor of 12}\}$
2. $N=\{n:n\text{is a factor of 24}\}$
3. $O=\{o:o\text{is a factor of 36}\}$
4. $P=\{p:p\text{is a factor of 48}\}$

Q. For the set $P=\{a,b,c,\{d,e\left\}\right\}$ tap on the bubbles having correct expressions related to the set $P.$

1. $\{d,e\}\in P$
2. $$ \{d,e\}\subset P$$
3. $\left\{\right\{d,e\left\}\right\}\subset P$
4. $b\in P$
5. $b\subset P$
6. $\left\{a,b,c\right\}\subset P$
7. $\left\{a,b,c\right\}\in P$
8. $\left\{a,b,d\right\}\subset P$
9. $\varphi \in P$
10. $\varphi \subset P$

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

1. False
2. True

Q. If A and B are subsets of the universal set U, then which of the following is/are true?

1. A ⊂ (A ∪ B)
2. A ⊂ B ⇔ (A ∪ B) = B
3. (A ∩ B) ⊂ A
4. A - B = (A ∪ B')

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.

Complete by evaluating each expression

$\frac{z}{3}-1$ for $z=6$

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. If a set A has n elements, then the total number of subsets of A is

1. $n$
2. $n^2$
3. $2^n$
4. $2n$

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 $X=\{x:x=8^n-7n-1|n\in N\}$ and $Y=\{y:y=49n-49|n\in N\}$

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

Q. For a given set $X=\{2,4,6\},$ tap the bubbles having a subset of $X.$

1. $\varnothing$
2. $\left\{2\right\}$
3. $\left\{4\right\}$
4. $\left\{4\right\}$
5. $\{2,4\}$
6. $\{2,6\}$
7. $\{2,6\}$
8. $\{2,4,6\}$

Q. For a given set $X=\{2,4,6\},$ tap the bubbles having a subset of $X.$

1. $\varnothing$
2. $\left\{2\right\}$
3. $\left\{4\right\}$
4. $\left\{4\right\}$
5. $\{2,4\}$
6. $\{2,6\}$
7. $\{2,6\}$
8. $\{2,4,6\}$

Q. Let A= {a, b, {c, d}, e}.
State, whether the following statement is true or false
(iii) {{c, d}} $\subset$ A

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 $X=\{x:x=8^n-7n-1|n\in N\}$ and $Y=\{y:y=49n-49|n\in N\}$

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