2017 · Q13
If A = (x : x is a multiple of 7}, B = x : x is a multiple of 5) and C = x : x is a multiple of 35, then which one of the following is a null set ?
Elementary MathematicsSet Theory
- A(A-B) ⋃ C
- B(A-B)-C
- C(A⋂B)⋂C
- D(A⋂B)-C
Explanation
A ∩ B is the set of multiples of both 7 and 5, i.e. multiples of 35 — exactly the set C. Hence (A ∩ B) − C = C − C = ∅, the null set: option D. The other options are non-empty (e.g. (A∩B) ∩ C = C).