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 Calculus Calculus Math Forum

 July 23rd, 2014, 07:29 AM #1 Newbie   Joined: Jul 2014 From: India Posts: 21 Thanks: 0 Relation there is a relation defined by xRy iff x-y+(2)^(1/2) is an irrational number the R is: 1) an equivalence relation 2) symmetric 3) transitive 4) none of these July 23rd, 2014, 08:43 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus xRx this means that $x-x+\sqrt{2}=\sqrt{2}$ is irrational, so the relation is reflexive. xRy this means that $x-y+\sqrt{2}$ is irrational but $y-x+\sqrt{2}$ is irrational too so the relation is symmetric. To prove that this relation is not transitive use $x=1$, $y=-\sqrt{2}$ and $z=\sqrt{2}$. $1\mathcal{R}\left(-\sqrt{2}\right)$, because $1-(-\sqrt{2})+\sqrt{2}=1+2\sqrt{2}$ is irrational. $\left(-\sqrt{2}\right)\mathcal{R}\left(\sqrt{2}\right)$ because $-\sqrt{2}-\sqrt{2}+\sqrt{2} =-\sqrt{2}$ which is irrational but $1\cancel{\mathcal{R}}\sqrt{2}$, $1-\sqrt{2}+\sqrt{2}=1$ is not irrational. Thanks from Rohit Kakkar Tags relation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post gaussrelatz Applied Math 3 August 31st, 2012 06:51 AM jaredbeach Algebra 3 August 21st, 2011 12:18 PM tbone1209 Algebra 1 January 10th, 2010 03:47 PM jaredbeach Calculus 0 December 31st, 1969 04:00 PM gaussrelatz Algebra 0 December 31st, 1969 04:00 PM

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