Answer:
option C.
G = {1, 2, 3}
H = {2, 4, 9}
1 = {4, 5, 6}
Step-by-step explanation:
From the diagram given above, we obtained the following information:
1. G Intercession H (G n H) has members i.e (G n H) is not epmty
G n H ≠ empty.
2. H Intercession I (H n I) has members i.e (H n I) is not empty
H n I ≠ empty.
3. G Intercession I (G n I) is empty i.e
G n I = empty.
Please note: Intercession of sets talks about elements or members common to the sets.
With the above information, we can suggest the answer to the question as follow:
For option A:
G = {odd numbers} = {1, 3, 5, 7,.. }
H = {even numbers} = {2, 4, 6, 8,.. }
I = {prime numbers} = {2, 3, 5, 7,...}
Therefore:
G n H = {} = empty
H n I = {2}
G n I = {3, 5, 7,..}
For option B:
G = {a,b,c}
H = {d, e, f}
I = {a, d, g}
Therefore:
G n H = {} = empty
H n I = {d}
G n I = {a}
For option C:
G = {1, 2, 3}
H = {2, 4, 9}
I = {4, 5, 6}
Therefore:
G n H = {2}
H n I = {4}
G n I = {} = empty
For option D:
G = {a, -13, 7}
H = {-13, -15, s}
I = {s, a, 23}
Therefore:
G n H = {-13}
H n I = {s}
G n I = {a}
From the above illustrations, only option C is correct.
