Question

State whether each of the following statement is true or false. Justify your answer.(i) `{ 2, 3,4, 5 }`and `{ 3, 6}`are disjoint sets,(ii) `{ a , e , i , o, u }`and `{ a , b , c , d }`are disjoint sets, (iii) `{2, 6, 10, 14}` and `{3, 7, 11, 15}` are disjoints sets (iv) `{2, 6, 10}` and `{3, 7, 11}` are disjoint sets.

Answer 1

(i) Element 3 is common in sets `{2,3,4,5} and {3,6}` Therefore, pair of sets is not disjoint
`rArr` Statement is false
(ii) Element `alpha` is common in sets `{a,e,i,o,u} and {a,b,c,d}`. Therefore, pair of sets is not disjoint
`rArr` Statement is false
(iii) There is no common element in the sets `{2,6,10,14} and {3,7,11,15}` Therefore, pair of sets is disjoint
`rArr` Statement is true
(iv) There is no common element in the sets `{2,6,10} and {3,7,11,15}`. Therefore, pair of sets is disjoint.
`rArr` Statement is true.