Power Set

Q. Which of the following is the power set of set A = { - 1, 0, 1 } ?

1. { {-1, 0}, {0, 1}, {-1, 1}, $\left\{\varphi \right\}$, {-1, 0, 1}}
2. {{1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, $\left\{\varphi \right\}$, {-1, 0, 1}}
3. {{1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, $\left\{\varphi \right\}$}
4. {{1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, {-1, 0, 1}}

Q. Derive : a raised to the the power of log X to the base a?

Q.

Write down the power set of $A=\{1,\left\{3\right\},4\}.$

Q.

A set S has 7 elements. How many subsets having at most 5 elements does it have?

1. 128

2. 125

3. 120

4. 116

Q. Assume that P (A) = P (B). Show that A = B.

Q. Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.

Q.

Let A = {1, 2} and B = {3, 4}, write $A\times B.$ How many sub sets will $A\times B$ have? List them.

Q. The number of elements in the power set of $A$, where $A=\{x:x\in W\text{and}{x}^3-1\le 7\}$

1. $3$
2. $16$
3. $8$
4. $64$

Q. The power set of the set $D=\varnothing$ is

1. $\left\{\varnothing \right\}$
2. $\varnothing$
3. $\left\{\right\{\varphi \left\}\right\}$

Q. For any set $A$ such that $n\left(A\right)=m,$ match the following:

1. $2^m$
2. $2^m-1$
3. $1$

Q.

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

1. $8$

2. $7$

3. $6$

4. $5$

Q. A set $A=\{b:b<5\&b\in I\}$, where $I$ denote integers, then tap on the correct bubbles.

1. $5\in A$
2. $6\in A$
3. $-6\in A$
4. $0\in A$
5. $3\in A$
6. $-336\in A$
7. $500\in A$
8. $-10\in A$
9. $-3\in A$