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.

rubinowyac

rubinowyac

Open question

2022-08-20

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.

Answer & Explanation

Kaeden Bishop

Kaeden Bishop

Beginner2022-08-21Added 15 answers

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).''

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