Question 13 (OR 2 nd question)
Check whether the relation R in the set R of real numbers, defined by R = {(a, b) : 1 + ab > 0}, is reflexive, symmetric or transitive.
Last updated at Oct. 1, 2019 by Teachoo
Question 13 (OR 2 nd question)
Check whether the relation R in the set R of real numbers, defined by R = {(a, b) : 1 + ab > 0}, is reflexive, symmetric or transitive.
Transcript
Question 13 (OR 2nd question) Check whether the relation R in the set R of real numbers, defined by R = {(a, b) : 1 + ab > 0}, is reflexive, symmetric or transitive. R = {(a, b) : 1 + ab > 0}, Checking for reflexive If the relation is reflexive, then (a ,a) ∈ R i.e. 1 + a2 > 0 Since square numbers are always positive Hence, 1 + a2 > 0 is true for all values of a. So, the given relation it is reflexive. R = {(a, b) : 1 + ab > 0}, Checking for symmetric, To check whether symmetric or not, If (a, b) ∈ R, then (b,a) ∈ R i.e., if 1+ ab < 0, then 1 + ba > 0 Since if 1 + ab > 0, then 1 + ba > 0 is always true for all value of a & b Hence, the given relation is symmetric R = {(a, b) : 1 + ab > 0}, Checking transitive To check whether transitive or not, If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R i.e., if 1 + ab > 0, & 1 + bc > 0, then 1 + ac > 0 Let’s take an example a = –8, b = –2, c = 1/4 1 + ab = 1 + (–8) × (–2)= 1 + 16= 17> 0 1 + bc = 1 + (–2) × 1/4= 1 – 1/2 = 1/2> 0 1 + ac = 1 + (–8) × 1/4= 1 – 2= –1≯ 0 Since 1 + ac ≯ 0 when 1 + ab > 0 and 1 + bc > 0 ∴ The condition is not true for all values of a, b, c. Hence, the given relation it is not transitive Therefore, the given relation is reflexive and symmetric, but not transitive
CBSE Class 12 Sample Paper for 2019 Boards
Question 1
Question 2
Question 3
Question 4 (Or 1st)
Question 4 (Or 2nd)
Question 5
Question 6
Question 7
Question 8 (Or 1st)
Question 8 (Or 2nd)
Question 9
Question 10 (Or 1st)
Question 10 (Or 2nd)
Question 11
Question 12 (Or 1st)
Question 12 (Or 2nd)
Question 13 (Or 1st)
Question 13 (Or 2nd) You are here
Question 14
Question 15
Question 16 (Or 1st)
Question 16 (Or 2nd)
Question 17
Question 18
Question 19
Question 20
Question 21 (Or 1st)
Question 21 (Or 2nd)
Question 22
Question 23
Question 24 (Or 1st)
Question 24 (Or 2nd)
Question 25
Question 26 (Or 1st)
Question 26 (Or 2nd)
Question 27 (Or 1st)
Question 27 (Or 2nd)
Question 28
Question 29
CBSE Class 12 Sample Paper for 2019 Boards
About the Author