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Given the following sets, select the statement below that is NOT true.
\n" ); document.write( "A = {r, i, s, k, e, d}, B = {r, i, s, e}, C = {s, i, r}
\n" ); document.write( "B ⊂ A or A ⊂ C or B ⊆ A or C ⊆ A or C ⊆ B
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document.write( "Let's go through them:\r\n" );
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document.write( "B ⊂ A\r\n" );
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document.write( "Substitute the actual sets for the capital letters that represent them.\r\n" );
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document.write( "{r, i, s, e} ⊂ {r, i, s, k, e, d}\r\n" );
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document.write( "That is true because all four elements listed on the left of this\r\n" );
document.write( "symbol ⊂ are all on the right of that symbol, and B doesn't contain\r\n" );
document.write( "all of A, so it's true that B is a proper subset of A. \r\n" );
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document.write( "A ⊂ C\r\n" );
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document.write( "Substitute the actual sets for the capital letters that represent them.\r\n" );
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document.write( "{r, i, s, k, e, d} ⊂ {s, i, r}\r\n" );
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document.write( "That is very false because the elements listed on the left of this\r\n" );
document.write( "symbol ⊂ are certainly not all on the right of that symbol, and B doesn't\r\n" );
document.write( "contain all of A, so it's false that B is a proper subset of A. \r\n" );
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document.write( "So that one is false\r\n" );
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document.write( "B ⊆ A\r\n" );
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document.write( "That means \"B ⊂ A or B = A\" and we've already shown that B ⊂ A is true above.\r\n" );
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document.write( "C ⊆ A\r\n" );
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document.write( "Substitute the actual sets for the capital letters that represent them.\r\n" );
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document.write( "{s, i, r} ⊆ {r, i, s, k, e, d}\r\n" );
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document.write( "That is true because all three elements listed on the left of this\r\n" );
document.write( "symbol ⊆ are all on the right of that symbol. The only difference\r\n" );
document.write( "between the symbols ⊆ and ⊂ is that the first one allows the set on\r\n" );
document.write( "the left to actually be equal to the set on the right. This symbol ⊂ \r\n" );
document.write( "does not. It requires that the set on the left have fewer elements \r\n" );
document.write( "than the one on the right.\r\n" );
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document.write( "------------------------------------ \r\n" );
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document.write( "C ⊆ B\r\n" );
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document.write( "Substitute the actual sets for the capital letters that represent them\r\n" );
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document.write( "{s, i, r} ⊆ {r, i, s, e}\r\n" );
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document.write( "That is true because all three elements listed on the left of this\r\n" );
document.write( "symbol ⊆ are all on the right of that symbol.\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "So A ⊂ C is the only one that's false.\r\n" );
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document.write( "Edwin\n" ); document.write( " \n" ); document.write( "