Sub Sets

For a given set D, which of the following is true

• D is a subset of itself.

• Number of subsets of D are $2^n$ where n is equal to number of elements in set D.

• $\phi$ is subset of D

• All of the above

B is a set such that n(B)=4. which of the following is not true

• Number of subsets of B =16

• Number of proper subsets of B =15

• Number of non empty proper sub sets of B =14

• none of the above

A={x, y, z, w }. Which of the following is not true.

• $\left\{y\right\}\ \in A$

• $x\in A$

• $\left\{w\right\}\subset A$

• $\phi\subset A$

If B= {2,4,6} then Power set of B i.e. P(B)=

• P(B) = {2,4,6,(2,4),(2,6), (4,6),(2,4,6), $\phi$ }

• P(B) = {{2},{4},{6},{2,4},{2,6}, {4,6},{2,4,6}, $\left\{\phi\right\}$ }

• P(B) = {{2},{4},{6},{2,4},{2,6}, {4,6},{2,4,6}, $\phi$ }

• none of the above

A={m,n ,p} and P(A) is power set of A. Which of the following is true?

• $\left\{m\right\}\in A$

• $n\subset A$

• $\left\{p\right\}\ \subset A$

• $\left\{\phi\right\}\subset A$

A = {3,5,7,9} and P(A) is power set of A. Which of the following is false?

• $3\in A$

• $\left\{5\right\}\in P\left(A\right)$

• $\left\{9\right\}\ \subset A$

• $\phi\in A$

A = {3,5,7,9} and P(A) is power set of A. Which of the following is false?

• $\phi\subset A$

• $\phi\in P\left(A\right)\in$

• $\phi\in A$

• $\phi\subset P\left(A\right)$

A = {x: x is a letter of the word BELLOW}

B ={x: x is a letter of the word ELBOW} then

• A is a proper sub set of B

• $A\ne B$

• B is a proper subset of A

• A is a subset of B

Which of the following is true?

• $\left\{x,y,z\right\}\subset\left\{x,y,z\right\}$

• $\left\{x,y,z\right\}\not\subseteq\left\{x,y,z\right\}$

• $\left\{x,y.z\right\}\subseteq\left\{x,y,z\right\}$

• None of these

Which of the following is not true ?

•  $\phi\in\left\{\phi\ \right\}$  

•  $\phi\subset\left\{\phi\ \right\}$  

•  $\left\{\phi\ \right\}\subseteq\left\{\phi\ \right\}$  

•  $n\left(\left\{\phi\right\}\right)=0$