ASSOCIATIVE PROPERTY OF SET WORKSHEET

Question 1 :

Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}.

Show that 

Au(BuC) = (AuB)uC

Also, verify the above using Venn diagram.

Question 2 :

Given A = {a, b, c, d}, B = {a, c, e} and C = {a, e}.

Show that

An(BnC) = (AnB)nC

Also, verify the above using Venn diagram.

Question 3 :

Verify Au(BuC) = (AuB)uC for the following three sets A, B and C.

A = {x : x is a prime factor of 42}

B = {x | 5 < x ≤ 12, x ∊ N}

C = {1, 4, 5, 6}

1. Answer :

Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}.

BuC = {3, 4, 5, 6} u {5, 6, 7, 8}

Buc = {3, 4, 5, 6, 7, 8}

Au(BuC) = {1, 2, 3, 4, 5} u { 3, 4, 5, 6, 7, 8}

Au(BuC) = {1, 2, 3, 4, 5, 6, 7, 8} ----(1)

AuB = {1, 2, 3, 4, 5} u {3, 4, 5, 6}

AuB = {1, 2, 3, 4, 5, 6}

(AuB)uC = {1, 2, 3, 4, 5, 6} u {5, 6, 7, 8}

= {1, 2, 3, 4, 5, 6, 7, 8} ----(2)

From (1) and (2),

Au(BuC) = (AuB)uC

Venn Diagram :

2. Answer :

Given A = {a, b, c, d}, B = {a, c, e} and C = {a, e}.

BnC = {a, c, e} n {a, e}

BnC = {a, e}

An(BnC) = {a, b, c ,d} n {a, e}

An(BnC) = {a} ----(1)

AnB = {a, b, c, d} n {a, c, e}

AnB = {a, c}

(AnB)nC = {a, c} n {a,e}

(AnB)nC = {a} ----(2)

From (1) and (2),

An(BnC) = (AnB)nC

Venn Diagram :

3. Answer :

A = {x : x is a prime factor of 42} ---> A = {2, 3, 7}

B = {x | 5 < x ≤ 12, x ∊ N} ----> B = {6, 7, 8, 9, 10, 11, 12}

C = {1, 4, 5, 6}

BuC = {6, 7, 8, 9, 10, 11, 12} u {1, 4, 5, 6}

BuC = {1, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Au(BuC) = {2, 3, 7} u {1, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Au(BuC) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} ----(1)

AuB = {2, 3, 7} u {5, 6, 7, 8, 9, 10, 11, 12}

AuB = {2, 3, 5, 6, 7, 8, 9, 10, 11, 12}

(AuB)uC = {2, 3, 5, 6, 7, 8, 9, 10, 11, 12} u {1, 4, 5, 6}

(AuB)uC = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} ----(2)

From (1) and (2),

Au(BuC) = (AuB)uC

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.