Team Gmath

Prove that 2 – √ 3 is irrational, given that √3 is irrational Solution:           Let 2 – √3 be a rational number. Then there exist positive integers ‘a’ and ‘ b’, where a and b are integers having no common factor other than 1 and b ≠ 0 such that … Read more

Prove that root 5 is an irrational number Solution:- Let us assume that on the contrary that √5 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒  Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 5 then also divisible by … Read more

Question 2: Check whether the relation R in R defined as R={(a, b): a ≤  b³} is reflexive, symmetric or transitive. Solution:-   Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric.  Transitive:- is not transitive. is neither reflexive nor symmetric nor transitive. Other question:- R= {(a, b): a ≤ b²} is neither reflexive … Read more

Question 1:-  Show that the relation R on the set R of real numbers, defined as R= {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive. Solution: We have, where a, b ∈ R Reflexivity:- Obiviously, is a real number and is not true. Therefore, R is not reflexive. Symmetric:- Let the … Read more