Suggest a universal set for the sets given below :

(i) {5, 7, 9}, {3, 5, 7}, {1, 3, 9} and {2, 4, 8}.

(ii) {odd numbers less than 8}, {prime numbers less than 8} and {even numbers between 3 and 8}.

(iii) {vowels in English alphabet}, {consonants in English alphabet}.

(i) {5, 7, 9}, {3, 5, 7}, {1, 3, 9} and {2, 4, 8}.

Subsets = {5, 7, 9}, {3, 5, 7}, {1, 3, 9} and {2, 4, 8}.

The elements present across all sets are 1, 2, 3, 4, 5, 7, 8, and 9.

∴ Universal Set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

(ii) {odd numbers less than 8}, {prime numbers less than 8} and {even numbers between 3 and 8}.

Subsets = {odd numbers less than 8}, {prime numbers less than 8} and {even numbers between 3 and 8}

Odd numbers less than 8 = {1, 3, 5, 7}

Prime numbers less than 8 = {2, 3, 5, 7}

Even numbers between 3 and 8 = {4, 6}

The elements present across all sets are 1, 2, 3, 4, 5, 6, 7.

∴ Universal Set U = {1, 2, 3, 4, 5, 6, 7}

(iii) {vowels in English alphabet}, {consonants in English alphabet}.

Subsets = {vowels in English alphabet}, {consonants in English alphabet}.

The first set contains {a, e, i, o, u} and the second contains all other letters of the alphabet.

∴ Universal Set U = {x : x is a letter in English alphabet}.