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?

Jerold 2021-08-11 Answered
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.
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Expert Answer

Khribechy
Answered 2021-08-12 Author has 100 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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