Hello everyone,I would like to ask is there anybody can solve these questions?

1.)Let A = {a, b}.Does this table define a semigroup and monoid on A?

* a b a a b b a b

2.)Let S = {a,b}. Write the operation table for the semigroup (P(S), ∪).

I really do not have ideas on how to solve them,that is why I ask here.

Please explain briefly on how to do the questions,thanks!