Proper Subset

Q. If a set has 31 proper subsets, then the number of elements in the set is ______.

1. 5

Q.

No set is a proper subset of itself.

Q.

For 2 sets A, B, A is called a proper subset of B iff

1. A ⊂ B

2. A = B

3. A ≠ B

4. Both A & C

Q. Find the greatest number which divides $2011$ and $2623$ leaving remainders $9$ and $5$ respectively.

Q.

The number of proper subsets of the set A = {a, b, c, d} is

1. 6

2. 5

3. 8

4. 7

Q.

If a set has 63 proper subsets, then it contains___ elements.

1. 1

2. 5

3. 8

4. 6

Q.

difference between proper and im proper subset?

Q.

If a set has 7 proper subsets, then it contains ___ elements.

1. 3

2. 2

3. 4

4. 8

Q. Write the proper numbers in the boxes.

(1) ${\left(5\times 8\right)}^2=5^{\boxed{}}\times 8^{\boxed{}}$
(2) ${\left[\left(\frac{3}{7}\right)\times \left(\frac{7}{9}\right)\right]}^3={\left(\frac{3}{7}\right)}^{\boxed{}}\times {\left(\frac{7}{9}\right)}^{\boxed{}}$
(3) ${\left[\left(\frac{-2}{3}\right)\times \left(\frac{-5}{11}\right)\right]}^4={\left(\frac{-2}{3}\right)}^{\boxed{}}\times {\left(\frac{-5}{11}\right)}^{\boxed{}}$
(4) ${\left(xy\right)}^{10}=x^{\boxed{}}\times y^{\boxed{}}$
(5) ${\left(pq\right)}^4=p^{\boxed{}}\times q^{\boxed{}}$

Q.

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

1. $8$

2. $7$

3. $6$

4. $5$

Q. If A and B are two non empty sets and A is proper subset of B. If n(A) =5, then minimum possible value of n(A symmetric difference B) is?

Q.

The number of non-empty subsets of the set $\{1,2,3,4\}$ is

1. 15

2. 14

3. 16

4. 17

Q. State whether the following statement is true or false:
Every set has a proper subset.

1. True
2. False

Q. Write the proper numbers in the boxes.

(7) ${\left(\frac{1}{3}\right)}^8\times {\left(\frac{1}{3}\right)}^6=\boxed{}{}^{\boxed{}}$

Q. Write the proper value in the boxes.

(1) $5^{-10}=\frac{1}{5^{\boxed{}}}$
(2) ${\left(\frac{1}{8}\right)}^{-4}=\frac{1}{{\left({\displaystyle \frac{1}{8}}\right)}^{\boxed{}}}$
(3) ${\left(-4\right)}^{-2}=\frac{1}{{\left(-4\right)}^{\boxed{}}}$
(4) ${12}^{-9}=\frac{1}{{12}^{\boxed{}}}$

Q.

If a set has 7 proper subsets, then it contains ____ elements.

1. 2

2. 3

3. 4

4. 8

Q.

If a set has 31 proper subsets, then the number of elements in the set is ___.

1. 4

2. 5

3. 6

4. 7

Q. If $A$ is a proper subset of $B$, then $n\left(A\right)$$n\left(B\right)$.

1. $<$
2. $>$
3. $=$

Q. Write the proper numbers in the boxes.

(3) ${\left(\frac{4}{5}\right)}^{11}\times {\left(\frac{4}{5}\right)}^2={\left(\frac{4}{5}\right)}^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(6) $m^2\times m^7=m^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(8) $p^4\times p^4={\boxed{}}^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(4) ${\left(-3\right)}^{15}\times {\left(-3\right)}^{10}={\left(-3\right)}^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(1) $2^8\times 2^3=2^{\boxed{}+\boxed{}}$

Q. Write the proper numbers in the boxes.

(2) ${\left(\frac{6}{11}\right)}^4\times \left(\frac{6}{11}\right)={\left(\frac{6}{11}\right)}^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(1) ${\left[{\left(-2\right)}^3\right]}^4={\left(-2\right)}^{\boxed{}\times \boxed{}}$
(2) ${\left[{\left(-\frac{12}{13}\right)}^2\right]}^5={\left(-\frac{12}{13}\right)}^{\boxed{}}$
(3) ${\left({10}^5\right)}^6=10{}^{\boxed{}}$
(4) ${\left[{\left(\frac{5}{3}\right)}^{10}\right]}^3={\left(\frac{5}{3}\right)}^{\boxed{}}$
(5) ${\left(x^5\right)}^7=x^{\boxed{}}$
(6) ${\left(m^4\right)}^4=m^{\boxed{}}$

Q. Write the proper numbers in the boxes.

(5) ${\left(5.7\right)}^4\times {\left(5.7\right)}^2={\left(5.7\right)}^{\boxed{}}$

Q. If every element of set A is an element of another set B, then A is a _______of B.

1. subset
2. image
3. Inverse
4. none of these

Q.

The number of proper subsets of the set {1, 2, 3} is

1. 8

2. 6

3. 5

4. 7