Question

If A = {x : x is an even natural number and x < 12}, 

B = {x : x is a natural number and divisor of 6}, 

then find i) (A ∪ B) – (A ∩ B), 

ii) (A – B) ∪ (B – A) What do you notice ?

Answer 1

A = {2, 4, 6, 8, 10}; B = {1, 2, 3, 6} 

A ∪ B = {2, 4, 6, 8, 10} ∪ {1, 2, 3, 6} = {1,2,3,4,6,8,10}

A ∩ B = {2, 4, 6, 8, 10} ∩ {1, 2, 3, 6} = {2, 6} 

(A ∪ B) – (A ∩ B) = {1, 2, 3, 4, 6, 8, 10} – {2,6} = {1,3,4,8,10} 

A – B = {2,4, 6, 8, 10} -{1,2, 3, 6}.  = {4, 8, 10} 

B – A = {1,2, 3, 6}-{2, 4, 6, 8, 10} = {1,3} 

(A – B) ∪ (B – A)- {4, 8, 10} ∪ {1,3} = {1,3,4, 8, 10} 

Noticed that (A ∪ B) – (A ∩ B) = (A – B) ∪ (B – A)