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Q9

Using venn diagrams, verify the following results.

**(i) A∩B ^{c}=A iff A∩B=Φ**

SOLUTION:

The region of vertical lines represents the set A while the region of horizontal lines represent the set B^{c}.The region of rectangles represents the A∩B^{c} which is the region of A,so A∩B^{c}=A iff A∩B=Φ

**(ii) (A-B)UB=AUB**

SOLUTION:

The region of horizontal line represents A and the region of vertical lines represents B. These two regions represent (A-B)UB and AUB,So (A-B)UB=AUB

**(iii) (A-B)∩B=Φ**

SOLUTION:

The region of horizontal lines represents A and the region of vertical lines represents B.Thus, the region of horizontal lines represents A-B.There is no region to represent (A-B)∩B,therefore, (A-B)∩B=Φ

**AUB=AU(A ^{c}∩B) **

SOLUTION:

The region of horizontal lines represents A^{c}.The doubly lined region represents A^{c}∩B.The shaded region and the doubly lined region represent Au(A^{c}∩B).

The shaded region and the vertical lined region represent AUB. Since the two reions are same so,AUB=Au(A^{c}∩B)