Ex 1.1, 7 - Chapter 1 Class 12 Relation and Functions

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Ex 1.1, 7 Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation. R = {( x, y): x and y have same number of pages} Check reflexive If reflexive, then (x, x) ∈ R Book x and Book x have the same number of pages. Which is always true. ∴ Hence, R is reflexive Check symmetric If x and y have the same number of pages, then we can say that y and x have the same number of pages. Hence If (x, y) ∈ R, then (y, x) ∈ R ∴ R is symmetric. Check transitive If x and y have the same number of pages. & y and z have the same number of pages. then, x and z have the same number of pages. Hence , If (x, y) ∈ R & (y, z) ∈ R , then (x, z) ∈ R ∴ R is transitive Since R is reflexive, symmetric and transitive Hence, R is an equivalence relation.