3 years ago
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
Joanna Staff answered 3 years ago
Joanna Staff answered 3 years ago
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).