Question

If A={2x : x ∈N and 1≤x < 4}, B ={(x+2) : x ∈N and 2≤x < 5} and C ={x : x ∈ N and 4 < x < 8}, find: (i) A∩B (ii) A∪B (iii) (A∪B)∩C

Answer 1

Answer:

(i). A∩B = { 4 , 6 }

(ii). AUB = { 2 , 4 , 5 , 6 }

(iii). (AUB)∩C = { 5 , 6 }

Solution:

Here ,

The given sets in set builder form are as follow ;

A = {2x : x ∈N and 1≤x < 4}

B ={(x+2) : x ∈N and 2≤x < 5}

C ={x : x ∈ N and 4 < x < 8}

Thus,

The given sets in roster form will be as follow ;

A = { 2 , 4 , 6 }

B = { 4 , 5 , 6 }

C = { 5 , 6 , 7 }

(i). A∩B

=> A∩B = { 2 , 4 , 6 } ∩ { 4 , 5 , 6 }

=> A∩B = { 4 , 6 }

(ii). AUB

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

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

(iii). (AUB)∩C

=> (AUB)∩C = { 2 , 4 , 5 , 6 } ∩ { 5 , 6 , 7 }

=> (AUB)∩C = { 5 , 6 }