Universal Sets and Venn Diagram

Question

a) If given sets A, and B, how can I draw the Venn diagram of the operation A∩B = ∅?

b) If A, B and C are sets, how can I show that A∩(B∪C) = (A∩B)∪(A∩C)

c) If A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15} C = {5, 10, 15, 20} and U is the set of all whole numbers less than or equal to 20, how can I draw a Venn diagram showing the relation of U, A, B and C?

Answer 1

A. Draw two circles that have no overlap.

B. Draw two Venn diagrams with sets A, B, and C.

First shade one diagram with BUC shaded,followed by its intersection with A shaded a different way.

Then shade the second diagram with A intersecting B and A intersecting C; then display this as a union.

Note that these two diagrams iindicate the same areas.

C. Outside the sets A, B, and C, put the numbers 0, 1, 7, 11, 13, 14, 16, 17, 18,and 19.

Draw circles A, B, and C with overlaps for A, B, and C.

Also, overlaps for A and B but not C, B and C but not A, and A and C but not B.

Also make A only, B only, and C only areas available.

A only: 2, 4, and 8.

B only: 3 and 9.

C only: 5 and 10.

A and B only: 6 and 12.

B and C only: 15.

There is nothing in the area for A, B, and C.

A and C only: 20.