Ex 1.1
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
Ex 1.1, 8
Ex 1.1, 9 (i)
Ex 1.1, 9 (ii) You are here
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)
Last updated at April 16, 2024 by Teachoo
Ex 1.1, 9 Show that each of the relation R in the set A = {x ∈ Z: 0 ≤ x ≤ 12} , given by (ii) R = {(a, b): a = b} is an equivalence relation. Find the set of all elements related to 1 in each case. A = {x ∈ Z: 0 ≤ x ≤ 12} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} R = {(a, b) : a = b} Check reflexive Since a = a is always true, So, (a, a) ∈ R, ∴ R is reflexive. Check symmetric We know that If a = b, then b = a Hence, if (a, b) ∈ R, then (b, a) ∈ R Hence, R is symmetric Check transitive If a = b & b = c, then a = c If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R Hence, R is transitive Hence, R is reflexive, symmetric and transitive, ∴ it is equivalence relation We need to find set of elements related to 1 R = {(a, b) : a = b} All elements related to 1 means a = 1, If a = 1, then b = a = 1 ∴ Only (1, 1) satisfies the relation. Hence, the set of elements related to 1 is {1}.