Find an example of a topological space that is seperable and first countable but not second countable. Explain your answer.

Determine whether the set S={1,x2,2+x2} spans P2.

Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?

Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.