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Pairs of SetsCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! If there is some relation between two sets such sets are called pairs of sets.Pairs of sets are equal sets, equivalent sets, disjoint sets and overlapping sets. Equal sets Two sets are said to be equal, if they contain the same elements. Examples: 1) A = { 1, 2, 3 } and B = { 1, 2, 3 } As the two sets contain the same elements so set A and set B are equal sets It is denoted as A = B Equivalent sets Two sets are equivalent if and only if, a one to one correspondence exists between them Examples As set A and set B are equivalent sets. It is denoted as A ↔ B 2) A = { x  x ∈ N, x ∠ 5 } and B = { x  x is a letter word DEAR} Solution: A = { x  x ∈ N, x ∠ 5 } A = { 1, 2, 3, 4 } B = { D, E, A, R} N(A) = n(B) ∴ A ↔ B Disjoint sets Two sets are disjoint, if they have no element in common. Examples : 1) A = { 1, 2, 3} and B { 4, 5, 6} Set A and set B are disjoint since there is no common element in them. 2) A {xx ∈ N} and B {x  x ∠ o, x ∈ Z} Solution: A = {xx ∈N} A = { 1, 2, 3, 4 …} B = { xx ∠o , X ∈ Z} B = {1, 2, 3 … } As there is no common element in set A and set B, So they are disjoint Overlapping Sets If two sets A and B have some elements in common then they are called overlapping sets Examples: 1) A = { 2, 3, 4} and B = {3, 4, 5} In set A and set B there are two common elements 3 and 4 Set A and set B are overlapping sets 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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