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Ex 1.1, 7 - Chapter 1 Class 12 Relation and Functions
Last updated at June 5, 2023 by Teachoo
Ex 1.1
Ex 1.1, 1 (i)
Ex 1.1, 1 (ii)
Ex 1.1, 1 (iii) Important
Ex 1.1, 1 (iv)
Ex 1.1, 1 (v)
Ex 1.1, 2
Ex 1.1, 3
Ex 1.1, 4
Ex 1.1, 5 Important
Ex 1.1, 6
Ex 1.1, 7 You are here
Ex 1.1, 8
Ex 1.1, 9 (i)
Ex 1.1, 9 (ii)
Ex 1.1, 10 (i)
Ex 1.1, 10 (ii)
Ex 1.1, 10 (iii) Important
Ex 1.1, 10 (iv)
Ex 1.1, 10 (v)
Ex 1.1, 11
Ex 1.1, 12 Important
Ex 1.1, 13
Ex 1.1, 14
Ex 1.1, 15 (MCQ) Important
Ex 1.1, 16 (MCQ)
Transcript
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.
