1Hmmm....i was able to think of the counter example...but to be frank i was looking for how to "WRITE PROOF" formally!
5 Answers
341Perhaps because a simple counterexample would dispose of it.
Take A = {1}, B={2}.
Then \{1,2\} \in P(AUB) but
\{1,2 \} \notin P(A) \bigcup P(B)
You would see {{1},{2}} but of course you know how to distinguish it from {1,2}
1341Well then the proof is staring in your face.
The set A \bigcup{} B is not an element of P(A) \bigcup{} P(B) but does belong to P(A \bigcup{} B)
341Also there is nothing illegitimate in disproving a statement by furnishing a counterexample.