Solution

The correct answer is option 1.

Key Points

(A) its worst-case running time is O(g(n)) and its best-case running time is Ω(g(n)).(O = big O)

True,

Big-Oh(O) denotes upper bound or worst case. 
Big-Omega(Ω) denotes lower bound or best case.
Big-Theta(Θ)  denotes Average bound or average case.

(B) its worst-case running time is Ω(g(n)) and its best-case running time is O(g(n)).(O = big O)

False, worst case should be Big-oh and best case should be Big-Omega

(C) O(g(n)) = Ω(g(n))(O = big O)

False, Can not cover  Big-Omega.