Question

For any sets a and b , prove that : p(a) u p(b) is subset p(aub)

Answer 1

$\textbf{Given:}$

$\text{A and B are two sets}$

$\textbf{To prove:}$

$\wp(A)\cup\wp(B)\;{\subseteq}\;\wp(A{\cup}B)$

$\text{Here, \wp(A) is power set of A}$

$\text{Let C\,{\in}\,\wp(A)\cup\wp(B) }$

$\implies\;C\,{\in}\,\wp(A)\;\text{or}\;C\,{\in}\,\wp(B)$

$\implies\;C\,{\subseteq}\,A\;\text{or}\;C\,{\subseteq}\,B$

$\implies\;C\,{\subseteq}\,A{\cup}B$

$\implies\;C\,{\in}\,\wp(A{\cup}B)$

$\therefore\bf\wp(A)\cup\wp(B)\,{\subseteq}\,\wp(A{\cup}B)$

$\textbf{Hence proved}$

$\textbf{Find more:}$

If the number of non-empty subsets of a set is 4095 then the number of elements of the set is option A 10 option b 11 options C12 option d13​

https://brainly.in/question/13119955

Answer 2

Answer:

Step-by-step explanation: