Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 1.1, 14 Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4 . R = {(L1, L2) : L1 is parallel to L2} Check reflexive Line L is parallel to itself So, line L is parallel to line L So, (L, L) ∈ R ∴ R is reflexive Check symmetric If L1 is parallel to L2 ,then L2 is parallel to L1. So, if (L1, L2) ∈ R, then (L2, L1) ∈ R ∴ R is symmetric. Check transitive If L1 is parallel to L2, and L2 is parallel to L3 , then L1 is parallel to L3. So, If (L1, L2) ∈ R, (L2, L3) ∈ R , then (L1, L3) ∈ R ∴ R is transitive. Hence, R is equivalence relation Find the set of all lines related to the line y = 2x + 4 . R = {(L1, L2) : L1 is parallel to L2} Set of all lines related to y = 2x + 4, is set of all lines that are parallel to y = 2x + 4. Let equation of line parallel to y = 2x + 4 be y = mx + c , where m is the slope of line Since y = 2x + 4 & y = mx + c are parallel, Slope of (y = 2x + 4) = Slope of (y = 2x + 4) 2 = m i.e. m = 2 Hence, the required line is y = mx + c i.e. y = 2x + c where c ∈ R.

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

Ex 1.1, 8 Important

Ex 1.1, 9 (i) Important

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 You are here

Ex 1.1, 15 (MCQ) Important

Ex 1.1, 16 (MCQ)

Chapter 1 Class 12 Relation and Functions (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.