Assessment – Complement of sets

ASSESSMENT

1.  If A = { 1, 2, 3, 4} and U = { 1, 2, 3, 4, 5, 6, 7, 8} then find A complement ( A’).
2. If B = { x | x is a book on Algebra in your library} . Find B’.
3. If A = { 1, 2, 3, 4, 5 } and U = N , then find A’.
4.  If A = { x | x is a multiple of 3, x ∉ N }. Find A’

ANSWERS

1. A = { 1, 2, 3, 4} and Universal set = U = { 1, 2, 3, 4, 5, 6, 7, 8}Complement of set A contains the elements present in universal set but not in set A.

Elements are 5, 6, 7, 8.

∴ A complement = A’ = { 5, 6, 7, 8}.

1. B’ = { x | x is a book in your library and x ∉ B }
2. A = { 1, 2, 3, 4, 5 }U = N

⇒ U = { 1, 2, 3, 4, 5, 6, 7, 8, 9,10,… }

A’ = { 6, 7, 8, 9, 10, … }

1. As a convention, x ∉ N in the bracket indicates N is the universal set.N = U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, … }

A = { x | x is a multiple of 3, x ∉ N }

A = { 3, 6, 9, 12, 15, … }

So, A’ = { 1, 2, 4, 5, 7, 8, 10,11, … }