Question

If A = {x : x ∈ N, 2 ≤ x ≤ 9} and B = {x : x is two digits natural number, sum of which digits is 8}, then find the following sets: 

(i) A ∪ B 

(ii) A ∩ B 

(iii) A – B 

(iv) (A – B) ∪ (B – A)

Answer 1

A = {x : x ∈ N, 2 ≤ x ≤ 9} = {2, 3, 4, 5, 6, 7, 8, 9} 

B = {x : x two digit natural number, sum of whose digits is 8} 

= {17, 26, 35, 44, 53, 62, 71} 

(i) A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9} ∪ {17, 26, 35, 44, 53, 62, 71} 

A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9, 17, 26, 35, 44, 53, 62, 71} 

(ii) A ∩ B = {2, 3, 4, 5, 6, 7, 8, 9} ∩ {17, 26, 35, 44, 53, 62, 71} = Φ 

(iii) A – B = {2, 3, 4, 5, 6, 7, 8,9} – {17, 26, 35, 44, 53, 62, 71} 

= All elements of A which arc not present in B. 

= {2, 3, 4, 5, 6, 7, 8, 9} = A 

(iv) (A – B) ∪ (B – A) 

A – B = {2, 3, 4, 5, 6, 7, 8, 9} 

B – A = {17, 26, 35, 44, 53, 62, 71} 

(A – B) ∪ (B – A) = {2, 3, 4, 5, 6, 7, 8, 9, 17, 26, 35, 44, 53, 62, 71} = A ∪ B