Q. Let A= {a, b, c, e, f, g}, B= {b, c, d, f, g, h} and C = {c, d, e, g, h, i}. The value of ((A – B) – (A – C) – (C – B)) is:

Correct Answer: (B) ∅

Explanation:

1. Given Sets:
– A = {a, b, c, e, f, g}
– B = {b, c, d, f, g, h}
– C = {c, d, e, g, h, i}

2. Calculate A – B:
– Elements in A but not in B: {a, e}

3. Calculate A – C:
– Elements in A but not in C: {a, b, f}

4. Calculate (A – B) – (A – C):
– Subtract A – C from A – B: {a, e} – {a, b, f} = {e}

5. Calculate C – B:
– Elements in C but not in B: {e, i}

6. Final Calculation {e} – {e, i}:
– Subtract C – B from the previous result: {e} – {e, i} = ∅
Therefore, the value of ((A – B) – (A – C) – (C – B)) is ∅.

Answer: (B) ∅