Question

Let A={x|x is even},B= 1 ,2,3,......,99,100},C={3,5,7,9} D={101,102} and E={101,103,105}.which of these sets can equal S if SA and S and B are disjoint? a.)A,b.)B,c.)C,d.)D,e.)E

Answer 1

If S and A disjoint then S cant be equal to A because a intersection with A is not empty. B is also disjoint to S then S cant be equal to B.

Suppose that $S = C$ but intersection of B and C is equal to $\{3,5,7,9\}$. So S and B are not disjoint. We get contradiction.

Suppose that $S = D$ then intersection of $D$ and $A$ is $\{102\}/$ so $S$ and $A$ are not disjoint. We get contradiction. And finally if $S = E$ then intersection of $A$ and $S$ equals to empty set and intersection of $B$ and $S$ equals to empty set. So $E$ can equal to $S$.

Correct answer is e) E.