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

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 You are here

Ex 1.1, 15 (MCQ) Important

Ex 1.1, 16 (MCQ)

Last updated at April 17, 2024 by Teachoo

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.