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Complement of SetCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! The complement of set A, denoted by A’ , is the set of all elements in the universal set that are not in A. It is denoted by A’Some Properties of Complement Sets 1) A ∪ A′ = U 2) A ∩ A′ = Φ 3) Law of double complement : (A′ )′ = A 4) Laws of empty set and universal set Φ′ = U and U′ = Φ. Examples : 1) If A = { 1, 2, 3, 4} and U = { 1, 2, 3, 4, 5, 6, 7, 8} then find A complement ( A’). Solution : 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}. 2) If B = { x  x is a book on Algebra in your library} . Find B’. Solution : B’ = { x  x is a book in your library and x ∉ B } 3) If A = { 1, 2, 3, 4, 5 } and U = N , then find A’. Solution : 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, … } 4) If A = { x  x is a multiple of 3, x ∉ N }. Find A’. Solution : 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, … } Set Theory • Sets • Representation of Set • Cardinal Number • Types of Sets • Pairs of Sets • Subset • Complement of Set • Union of the Sets • Intersection of Sets • Operations on Sets • De Morgan's Law • Venn Diagrams • Venndiagrams for sets • Venndiagrams for different situations • Problems on Intersection of Two Sets • Problems on Intersection of Three Sets Covid19 has affected physical interactions between people. Don't let it affect your learning.
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