Consider the following statement:
” A is a subset of B. Therefore A is a subset of P(B).”
This statement is incorrect as written. Assuming the first sentence is true, what is incorrect about the second sentence? State the second sentence correctly.

1 Answers

Best Answer

Since given statement is :

"" A is subset of B. Therefore A is subset of P(B)""

Concept:

First we have to understand what is the means of P(B).

P(B) = power set of B

= Set of all subset of B

Let us understand by an example

If

B= {1,2}

Then

P(B)= { {}, {1},{2}, {1,2}}

Since First statement is

A is subset of B.

It implies that

Power set of A is subset of power set of B

It implies that

"" P(A) is subset of P(B).

So instead of

"" A is subset of P(B)"".

Correct statement is.

""P(A) is subset of P(B).""

So combined statement is:

A is subset of B.Therefore P(A) is subset of P(B).

"" A is subset of B. Therefore A is subset of P(B)""

Concept:

First we have to understand what is the means of P(B).

P(B) = power set of B

= Set of all subset of B

Let us understand by an example

If

B= {1,2}

Then

P(B)= { {}, {1},{2}, {1,2}}

Since First statement is

A is subset of B.

It implies that

Power set of A is subset of power set of B

It implies that

"" P(A) is subset of P(B).

So instead of

"" A is subset of P(B)"".

Correct statement is.

""P(A) is subset of P(B).""

So combined statement is:

A is subset of B.Therefore P(A) is subset of P(B).