Let E, F and G be finite sets. Let X = (E ∩ F) - (F ∩ G) and Y = (E - (E ∩ G))…
2006
Let E, F and G be finite sets. Let X = (E ∩ F) - (F ∩ G) and Y = (E - (E ∩ G)) - (E - F). Which one of the following is true?
- A.
X ⊂ Y
- B.
X ⊃ Y
- C.
X = Y
- D.
X - Y ≠ φ and Y - X ≠ φ
Attempted by 392 students.
Show answer & explanation
Correct answer: C
Simplify X:
X = (E ∩ F) - (F ∩ G) = E ∩ F ∩ G^c.
Simplify Y:
First, E - (E ∩ G) = E ∩ G^c.
Then subtract (E - F) = E ∩ F^c: (E ∩ G^c) - (E ∩ F^c) = E ∩ G^c ∩ F = E ∩ F ∩ G^c.
Conclusion: X = Y = E ∩ F ∩ G^c.
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