document.write( "Question 1191032: Determine if the following are equivalence relations:
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Algebra.Com's Answer #822837 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "Determine if the following are equivalence relations:
\n" ); document.write( "1. S=ℝ
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\n" ); document.write( "(a,b)∈R if a=b+1
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document.write( "A relation R is called \"equivalence\",  if for any pair (a,b) belonging to R,  the inverted pair (b,a) also belongs to R.\r\n" );
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document.write( "Consider the pair (a,b) = (2,1).               We have 2 = 1 + 1, so the pair (2,1) belongs to R.\r\n" );
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document.write( "Now consider the inverted pair (b,a) = (1,2).  We have  1 =/= 2+1, therefore the pair (b,a) does not belong to R.\r\n" );
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document.write( "It shows and proves that R is not an equivalence relation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained by presenting a counter-example.\r
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