document.write( "Question 1126783: Is the following relation (R) symmetric or not? Explain.\r
\n" ); document.write( "\n" ); document.write( "R={(x,y)∈Z×Z:x^2+y^2=1} where Z is the set of integer numbers. \n" ); document.write( "

Algebra.Com's Answer #743132 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "This relation is symmetric.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To check it, you should make sure that if (x,y) is the relation, then (y,x) is the relation, too.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the terms of the given relation, it means to check that \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    if  x^2 + y^2 = 1,  where x and y are integer, then  y and x are integer, too,  and  y^2 + x^2 = 1,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "but it is clearly obvious (follows from the commutative property of adding integer numbers).\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Answered and proved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "==============\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "By the way, the only pairs of this relation are\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    (1,0)\r\n" );
document.write( "    (-1,0)\r\n" );
document.write( "    (0,1)\r\n" );
document.write( "    (0,-1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Not so many . . . - because your relation is defined over integer numbers . . . \r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );