Advertisement Remove all ads
Advertisement Remove all ads
Diagram
From the given diagram, find :
(i) (A ∪ B) - C
(ii) B - (A ∩ C)
(iii) (B ∩ C) ∪ A
Verify :
A - (B ∩ C) = (A - B) ∪ (A - C)
Advertisement Remove all ads
Solution
(i) A ∪ B = {a, b, c, d} ∪ {c, d, e, g}
= {a, b, c, d, e, g}
∴ (A ∪ B) - C = {a, b, c, d, e, g} - {b, c, e, f}
= {a, d, g}
(ii) (A ∩ C) = {a, b, c, d} ∩ {b, c, e, f}
= {b, c}
∴ B - (A ∩ C) = {c, d, e, g} - {b, c}
= {d, e, g}
(iii) B ∩ C = {c, e, d, g} ∩ {b, c, e, f}
= {c, e}
∴ A - (B ∩ C) = (A - B) ∪ (A - C)
⇒ (B ∩ C) = {c, e}
So, A − (B ∩ C) = {a, b, d} .....(1)
Now, A − B = {a, b}
And A − C = {a, d}
The union of two sets has the elements of both sets.
So, (A − B) ∪ (A − C) = {a, b, d} .....(2)
From (1) and (2), we have
A − (B ∩ C) = (A − B) ∪ (A − C)
The relation holds True.
Concept: Venn Diagram
Is there an error in this question or solution?
Advertisement Remove all ads
APPEARS IN
Advertisement Remove all ads