Equivalence Relation on Set Equivalence relation on set is a relation which is reflexive, symmetric and transitive. A relation R, defined in a set A, is said to be an equivalence relation if and only if (i) R is reflexive, that is, aRa for all a ∈ A. (ii) R is symmetric, that is,…
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Transitive Relation on Set What is transitive relation on set? Let A be a set in which the relation R defined. R is said to be transitive, if (a, b) ∈ R and (b, a) ∈ R ⇒ (a, c) ∈ R, That is aRb and bRc ⇒ aRc where a, b, c ∈…
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Anti-symmetric Relation on Set What is anti-symmetric relation onset? Let A be a set in which the relation R defined. R is said to be anti-symmetric, if there exist elements, if aRb and bRa ⇒ a = b that is, (a, b) ∈ R and ((b, a) ∈ R ⇒ a = b. A relation…
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Symmetric Relation on Set Here we will discuss about the symmetric relation on set. Let A be a set in which the relation R defined. Then R is said to be a symmetric relation, if (a, b) ∈ R ⇒ (b, a) ∈ R, that is, aRb ⇒ bRa for all (a, b) ∈ R.…
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Reflexive Relation on Set Reflexive relation on set is a binary element in which every element is related to itself. Let A be a set and R be the relation defined in it. R is set to be reflexive, if (a, a) ∈ R for all a ∈ A that is, every element of…
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Properties of Elements in Sets The following properties of elements in sets are discussed here. If U be the universal set and A, B and C are any three finite sets then; 1. If A and B are any two finite sets then n(A – B) = n(A) – n(A ∩ B) i.e. n(A –…
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Proof of De Morgan’s Law Here we will learn how to proof of De Morgan’s law of union and intersection. Definition of De Morgan’s law: The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection of two sets is equal to the…
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Laws of Algebra of Sets Here we will learn about some of the laws of algebra of sets. 1. Commutative Laws: For any two finite sets A and B; (i) A U B = B U A (ii) A ∩ B = B ∩ A 2. Associative Laws: For any three finite sets…
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Examples on Venn Diagram Solved examples on Venn diagram are discussed here. From the adjoining Venn diagram, find the following sets. (i) A (ii) B (iii) ξ (iv) A’ (v) B’ (vi) C’ (vii) C – A (viii) B – C (ix) A – B (x) A ∪ B (xi) B ∪ C (xii) A…
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Complement of a Set using Venn Diagram The complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A’ or AC C or U…
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