Question

if A={1,2,3,4},B ={3,4,5,6} and C={5,6,7,8} find (AUB)n(AUC)​

Answer 1

Answer :

(AUB)∩(AUC) = { 1 , 2 , 3 , 4 , 5 , 6 }

Note:

★ Set : A well defined collection of distinct objects is called a set .

★ Union of two sets : The union of two sets A and B is the set of all those elements which are either in A or in B or in both .

→ This set is denoted by A U B .

★ Intersection of two sets : The intersection of two sets A and B is the set of all those elements which are in common in both A and B .

→ This set is denoted by A ∩ B .

★ Difference of sets : The difference of two sets A and B in the order ( also called relative complement of B in A ) is the set of all those elements of A which are not the elements of B .

→ It is denoted by (A - B) .

Solution :

→ Given : A = { 1 , 2 , 3 , 4 }

B = { 3 , 4 , 5 , 6 }

C = { 5 , 6 , 7 , 8 }

→ To find : (AUB)∩(AUC)

Firstly ,

Let's find AUB and AUC .

Thus ,

=> AUB = { 1 , 2 , 3 , 4 } U { 3 , 4 , 5 , 6 }

=> AUB = { 1 , 2 , 3 , 4 , 5 , 6 }

Also ,

=> AUC = { 1 , 2 , 3 , 4 } U { 5 , 6 , 7 , 8 }

=> AUC = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

Now ,

(AUB)∩(AUC)

= { 1,2,3,4,5,6 } ∩ { 1,2,3,4,5,6,7,8 }

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

Hence ,

(AUB)∩(AUC) = { 1 , 2 , 3 , 4 , 5 , 6 }