Mathematics
Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} be the universal set and let A = {5, 7, 11, 13}, B = {6, 8, 10, 12, 14, 16} and C = {5, 6, 8, 10, 11, 12} be its subsets.
Find:
(i) A'
(ii) B'
(iii) C'
Answer
(i) A'
Universal Set (U) = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
Set A = {5, 7, 11, 13}
Remove 5, 7, 11, and 13 from U.
A' = {6, 8, 9, 10, 12, 14, 15, 16}
(ii) B'
Universal Set (U) = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
B = {6, 8, 10, 12, 14, 16}
Remove 6, 8, 10, 12, 14, and 16 from U.
B' = {5, 7, 9, 11, 13, 15}
(iii) C'
Universal Set (U) = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
C = {5, 6, 8, 10, 11, 12}
Remove 5, 6, 8, 10, 11, and 12 from U.
C' = {7, 9, 13, 14, 15, 16}
Related Questions
Which of the following statements are true ?
(i) {a} ⊂ {a, b, c}
(ii) {a} ⊂ {b, c, d, e}
(iii) Φ ⊂ {a, b, c}
(iv) Φ ∈ {a, b, c}
(v) 0 ∉ Φ
(vi) {1} ⊂ {0, 1}
(vii) Every subset of a finite set is finite.
(viii) Every subset of an infinite set is infinite.
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Write the subset of A containing :
(i) all odd numbers
(ii) all prime numbers
(iii) all multiples of 4.
Let the set I of all integers be the universal set and let A = {x : x is a negative integer} be its subset. Find A'.
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}.