Using venn diagrams, verify the following results.
(i) A∩Bc=A iff A∩B=Φ
The region of vertical lines represents the set A while the region of horizontal lines represent the set Bc.The region of rectangles represents the A∩Bc which is the region of A,so A∩Bc=A iff A∩B=Φ
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
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
The region of horizontal lines represents Ac.The doubly lined region represents Ac∩B.The shaded region and the doubly lined region represent Au(Ac∩B).
The shaded region and the vertical lined region represent AUB. Since the two reions are same so,AUB=Au(Ac∩B)