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Ex 1.1, 1 (iv) - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at March 22, 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) You are here
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
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)
Chapter 1 Class 12 Relation and Functions
Serial order wise
Transcript
Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (iv) Relation R in the set Z of all integers defined as R = {(x, y): x y is as integer} R = {(x, y): x y is as integer} Check Reflexive Since, x x = 0 & 0 is an integer x x is an integer (x, x) R R is reflexive Check symmetric If x y is an integer, then (x y) is also an integer, y x is an integer So, If x y is an integer, then y x is an integer i.e. If (x, y) R, then (y, x) R R is symmetric Check transitive If x y is an integer & y z is an integer then, sum of integers is also an integer (x y) + (y z) is an integer. x z is an integer. So, If x y is an integer & y z is an integer then, x z is an integer. If (x, y) R & (y, z) R , then (x, z) R R is transitive Hence, R is reflexive, symmetric, and transitive.
