DM - Functions & Relations -Q1

+1 vote

Consider the following statements(A and B are two sets) :

S1: If P(A) $\subseteq$ P(B)  then A $\subseteq$ B

S2: If  A $\subseteq$ B then P(A) $\subseteq$ P(B)

Which one of the above statements is TRUE?

(A). Only S1

(B). Only S2

(C). Both S1 and S2

(D). Neither S1 nor S2

reshown 6 days ago

C. Both are true.

same way you can try the second statement.

S 2 :  If  A $\subseteq$ B then P(A) $\subseteq$ P(B)

Since A is a subset of B, so, every element that is in A, is also in B. So, consider any subset of A, that will contain some elements of A, and all those elements are also in B, so, that subset is also a subset of B. Hence, P(A) $\subseteq$ P(B).

Or we can prove by contradiction as we proved S1.

https://math.stackexchange.com/questions/557300/prove-if-pa-is-a-subset-of-pb-a-is-a-subset-of-b

answered 4 days ago by (112,390 points)