Difference between revisions of "Subsets"
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== Definition == | == Definition == | ||
| − | Let <math>X</math> and <math>Y</math> be sets. We say that ''<math>X</math> is a subset of <math>Y</math>'' if every element of <math>X</math> is also an element of <math>Y</math> , and we write <math>X\subseteq Y</math> or <math>Y\supseteq X</math> . Symbolically, <math>X\subseteq Y</math> means <math>x\in X</math> <math>\Rightarrow</math> <math>x\in Y</math> . | + | Let <math>X</math> and <math>Y</math> be sets. We say that '''''<math>X</math> is a subset of <math>Y</math>''''' if every element of <math>X</math> is also an element of <math>Y</math> , and we write <math>X\subseteq Y</math> or <math>Y\supseteq X</math> . Symbolically, <math>X\subseteq Y</math> means <math>x\in X</math> <math>\Rightarrow</math> <math>x\in Y</math> . |
Two sets <math>X</math> and <math>Y</math> are said to be equal, <math>X=Y</math>, if both <math>X\subseteq Y</math> and <math>Y\subseteq X</math>. Note that some authors use the symbol <math>\subset</math> in place of the symbol <math>\subseteq</math>. | Two sets <math>X</math> and <math>Y</math> are said to be equal, <math>X=Y</math>, if both <math>X\subseteq Y</math> and <math>Y\subseteq X</math>. Note that some authors use the symbol <math>\subset</math> in place of the symbol <math>\subseteq</math>. | ||
Revision as of 19:27, 27 June 2015
Definition
Let and be sets. We say that is a subset of if every element of is also an element of , and we write or . Symbolically, means .
Two sets and are said to be equal, , if both and . Note that some authors use the symbol in place of the symbol .
