Proper Set

Q.

The number of proper subsets of the set $\{1,2,3\}$ is ___.

1. 7

2. 6

3. 5

4. 8

Q. Which of the following statements are true? Give reason to support your answer.
(i) For any two sets A and B either $A\subseteq B\mathrm{or}B\subseteq A;$
(ii) Every subset of an infinite set is infinite;
(iii) Every subset of a finite set is finite;
(iv) Every set has a proper subset;
(v) {a, b, a, b, a, b, ...} is an infinite set;
(vi) {a, b, c} and {1, 2, 3} are equivalent sets;
(vii) A set can have infinitely many subsets.

Q.

When is A called proper subset of B?

1. A ⊂ B

2. A = B

3. A ≠ B

4. Both A & B

5. Both A & C

Q. Set of natural numbers A = $A=\{x:xϵN\}$ is a proper subset of which of the following

1. Set of whole numbers $A_1=\{x:xϵW\}$
2. Set of Real numbers $A_2=\{x:xϵR\}$
3. Set of Integers $A_3=\{x:xϵI\}$
4. All of the above.

Q.

Which of the following are relations from the set $A=\{1,2,3,4\}$ to set $B=\{a,b,c\}$?

1. $\left\{\right(1,a),(1,b),(1,c\left)\right\}$

2. $\left\{\right(2,a),(2,b),(2,c\left)\right\}$

3. $\left\{\right(3,a),(3,b),(3,c\left)\right\}$

4. $\left\{\right(4,a),(4,b),(4,c\left)\right\}$

Q. If a set $A$ is a subset of set $B,$ this means each and every element of set $B$ is in set $A.$

1. False
2. True

Q. If $N$ is the set of all Natural Numbers, $W$ is the set of all Whole Numbers, $Z$ is the set of all Integers, $Q$ is the set of all Rational Numbers, $P$ is the set of all Irrational Numbers, $R$ is the set of all Real Numbers, then choose the correct option(s).

1. $N\subset Z\subset W\subset R$
2. $N\subset Z\subset P$
3. $N\subset Z\subset Q\subset R$
4. $N\subset W\subset Q\subset R;P\subset R$

Q. Examine whether the following statements are true or false:
(i) { $a,b$ } $\subset ̸$ { $b,c,a$ }
(ii) { $a,e$ } $\subset$ { $x:x$ is a vowel in the English alphabet}
(iii) { $1,2,3$ } $\subset$ { $1,3,5$ }
(iv) { $a$ }$\subset$ { $a,b,c$ }
(v) { $a$ }$ϵ$ { $a,b,c$ }
(vi) { $x:x$ is an even natural number less than $6$} $\subset$ { $x$ : x is a natural number which divides $36$ }

Q.

Is∅a proper subset or a improper subset of a superset ??

Q. 1 if A and B are two non empty sets and Ais proper subset of B. n(a)=5 , then minimum possible values of n(Asymmetric difference B) is ?

Q. Which of the following is the superset of rational numbers?

1. Natural numbers
2. Whole numbers
3. Real numbers
4. Integers
   

Q.

Write down all possible proper subsets each of the following sets:
(i) $\{1,2\}$
(ii) $\{1,2,3\}$
(iii) $\left\{1\right\}$.

Q.

The number of proper subsets of the set $\{1,2,3\}$ is ___.

1. 8

2. 7

3. 6

4. 5

Q.

Find the value of |-2| + |-1| + |0| + |1|

Q. If $N$ is a set of all natural numbers and $Q$ is a set of all rational numbers, then which of the following is a correct representation for these two sets?

1. 
2. 
3. 

Q. What is the number of ordered pair (A, B) where A and B are subsets of {1, 2, 3, 4, 5} such that neither A is a proper subset of B nor B is a proper subset of A?

Q. Q.4. Write down all possible proper subsets of the set {1, {2}}.

Q. Set of natural numbers A = $\{x:x\in N\}$ is a proper subset of which of the following

1. Set of whole numbers $A_1=\{x:xϵW\}$
2. Set of Real numbers $A_2=\{x:xϵR\}$
3. Set of Integers $A_3=\{x:xϵI\}$
4. All of the above.