In this section, there is a worksheet on intersection of three sets.
Worksheet on Intersection of 3 Sets
1. ξ is the set of points inside the given rectangle. List the elements of:
1. B ∩ C 2. A ∩ B ∩ C
3. (A∪ B)’ 4. (A ∪ B ∪ C)’ 5. A – B
2. Using the Venn diagram, list the elements of the following sets :
1. A ∩ B 2. C’ ∩ B ∩ A
3. ( A ∪ B ∪ C )’ 4. (A ∪ B) ∩ C 5. A – B 6. B – (A ∪ B)
3. Using set symbols, write down expressions for the shaded portion in the following Venn diagrams:
Hence prove that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
4. What sets do the shaded regions in the following diagrams represent?
5. Using the Venn diagrams to verify:
1. {c} = (A ∩ B) ∩ C’
2. A ∪ B ∪ C = ( A ∪ B) ∪ C = A ∪ (B ∪ C)
3. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
6.Draw a Venn diagram to represent three sets X, Y and Z such that X ∩ Y = Z. In the same diagram insert sets P and Q, such that X ∩ Y ⊂ P and X ∩ Y ⊃ Q. Is it true that X ∩ Y ∩ Z = Q ?
6. If A = { 1, 9, 10}
B = { 3,4,6,11,12}
C = { 2,5,6}
Verify A∪ (B∩ C) = (A∪ B) ∩ (A ∪ C)
8. In each of the diagrams given, shade the region which represents the set underneath the diagrams.