![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
\n" ); document.write( "A = {x | x is a sport that uses a ball}
\n" ); document.write( "B = {basketball, soccer, tennis}
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "A = B No A doesn't equal B because for instance, A contains baseball, golf,\r\n" );
document.write( "etc. but B doesn't.\r\n" );
document.write( "\r\n" );
document.write( "A ⊆ B No, every element of A is not an element of B because for\r\n" );
document.write( "instance, baseball is an element of A, \r\n" );
document.write( "\r\n" );
document.write( "B ⊆ A Yes because, although B doesn't equal A by any means, every\r\n" );
document.write( "element of B is also an element of A.\r\n" );
document.write( "\r\n" );
document.write( "A ⊂ B No, this is just like A ⊆ B except that A ⊆ B allows\r\n" );
document.write( "but does not require, the possibility of A = B, whereas A ⊂ B doesn't\r\n" );
document.write( "allow A = B. But that's not any worry here.\r\n" );
document.write( "\r\n" );
document.write( "B ⊂ A Yes because every element of B is also an element of A. The only\r\n" );
document.write( "difference between ⊂ and ⊆ is that ⊂ does NOT allow the sets\r\n" );
document.write( "on both sides of it to be exactly the same set, whereas ⊆ allows it but\r\n" );
document.write( "does not require it.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "So B ⊆ A and B ⊂ A are the only ones that hold.\r\n" );
document.write( "\r\n" );
document.write( "Examples:\r\n" );
document.write( "\r\n" );
document.write( "{a,r,t} = {t,a,r} is true because the order they're listed in doesn't matter\r\n" );
document.write( "{a,r,t} ⊆ {t,a,r} is true because ⊆ allows (but doesn't require)\r\n" );
document.write( "equality\r\n" );
document.write( "{a,r,t} ⊂ {t,a,r} is false because ⊂ does not allow equality\r\n" );
document.write( "{a,r,t} ⊂ {s,t,a,r} is true because every element of the left set is also\r\n" );
document.write( "an element of the right set. It doesn't allow equality but we surely don't\r\n" );
document.write( "have that.\r\n" );
document.write( "{a,r,t} ⊆ {s,t,a,r} is true because every element of the left set is also\r\n" );
document.write( "an element of the right set. It allows equality but doesn't require it.\r\n" );
document.write( "\r\n" );
document.write( "Edwin \n" );
document.write( "