Complexity

Question

Consider two natural-valued functions $f: \mathbb{N} \mapsto \mathbb{N}$, and $g: \mathbb{N} \mapsto \mathbb{N}$. Which of the following statements canNOT be True?

1. $f \in O(g)$ and $g \in O(f)$
2. $f \in \Theta(g)$ and $g \in \Theta(f)$
3. $f \in \Omega(g)$ and $g \in \Omega(f)$
4. $f \in O(g)$ but $g \notin \Omega(f)$

Comments

i think quetion was which of the foloowing is true. then b is true.

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no, it is "cannot".

Answer 1

f∈O(g) = f≤c.g(n)  g∈O(f) = g≤ c₁f(n)
if we take same function for both f and g then a b and c can be possible for some constant.
a) f∈O(g) and g∈O(f)
b) f∈Θ(g) and g∈Θ(f)
c) f∈Ω(g) and g∈Ω(f)
d) f∈O(g) but g∉Ω(f) 
f∈O(g) = f≤c.g(n) for some constant and it also implies that g∈Ω(f)  coz for some constant g≤ c.f(n) is possible 
so i think option D.