Regarding first statement :
(n + a)b = nb + bC1 nb-1 . a + bC2 nb-2 . a2 + ....................
= nb [ In asymptotics , we consider the dominant term only when addition terms are there ]
= Ώ(nb) and O(nb) and θ(nb) as well.
Hence the first statement is true.
Regarding the second statement :
If a = b , then
a + 1 > a and hence a + 1 > b
Hence na+1 = θ(nb) is false as theta notation means that both LHS and RHS may only differ by constant and not by any variable factor . But here LHS is 'n' times more than RHS which is not acceptable for theta notation.
Instead na+1 = Ώ(nb) is correct asymptotic notation for given LHS - RHS pair.Hence second statement is false.