Question

using Venn diagram verify the following properties of difference laws​

Answer 1

Answer:

Proof by venn diagram - Properties of set operations

Problem 1 :

For the given sets A = { -10, 0, 1, 9, 2, 4, 5 } and B = {-1, -2, 5, 6, 2, 3, 4 }, verify that

(i) Set union is commutative. Also verify it by using Venn diagram.

(ii) Set intersection is commutative. Also verify it by using Venn diagram.

Solution :

(i) Let us verify that union is commutative.

A u B = { -10, 0, 1, 9, 2, 4, 5 } u {-1, -2, 5, 6, 2, 3, 4 }

A u B = { -10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9 } ---------(1)

B u A = {-1, -2, 5, 6, 2, 3, 4 } u { -10, 0, 1, 9, 2, 4, 5 }

B u A = { -10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9 } ---------(2)

From (1) and (2), we have

A u B = B u A

By Venn diagram, we have

From the above two Venn diagrams, it is clear that

A u B = B u A

Hence, it is verified that set union is commutative.

(ii) Let us verify that union is commutative.

A n B = { -10, 0, 1, 9, 2, 4, 5 } n {-1, -2, 5, 6, 2, 3, 4 }

A n B = { 2, 4, 5 } ---------(1)

B n A = {-1, -2, 5, 6, 2, 3, 4 } u { -10, 0, 1, 9, 2, 4, 5 }

B n A = { 2, 4, 5 } ---------(2)

From (1) and (2), we have

A n B = B n A

By Venn diagram, we have