hello i need help to prove that this statement is either true or false . i already tried to prove it with an example and arrived to the conclusion that this statement is true . my question is how can i prove that it is true or false for any given set without a specific example . If |A|>4 Then |(A)|+|(B)| ≠ |(A∪B)|.
p.s: (A) and (B) are power sets
Hint: under what circumstances do there exist integers $a,b, c$ such that $2^a+2^b=2^c$?