document.write( "Question 1126782: Is the following relation a reflexive relation or not? Explain.\r
\n" ); document.write( "\n" ); document.write( "A={(x,y)∈RXR:x is less than or equal to y} where R is the set of real numbers.
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Algebra.Com's Answer #743135 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "    You are given the set of all real numbers R.\r\n" );
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document.write( "    You consider all the pairs (x,y) of real numbers such that  x <= y. It is your set A.\r\n" );
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document.write( "    The set A  is not  a primary set of the consideration.\r\n" );
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document.write( "    The primary set is R.\r\n" );
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document.write( "    And the question is:  IS IT TRUE THAT FOR EVERY x from R  the pair (x,x)  is in the relation A, i.e.  x <= x  ??\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now I am ready to answer.\r
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document.write( "This relation is reflexive.\r\n" );
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document.write( "To check it, you should make sure that for every real number x, the pair (x,x) is the relation.\r\n" );
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document.write( "In the terms of the given relation, it means to check that \r\n" );
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document.write( "    for each real x,  x <= x.\r\n" );
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document.write( "but it is clearly and obviously true for all real numbers.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answered and proved.\r
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\n" ); document.write( "\n" ); document.write( "If you have difficulties in understanding this issue, look into this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Reflexive_relation\r
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