LN4(Binary relation)(2) - BINARY RELATION Definition A...

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BINARY RELATION
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Definition . A binary relation on a set is any subset of . Example . Let . Then , (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} By definition, a binary relation on is any subset of . Therefore, the following are binary relations on the set : Note : There are exactly binary relations on the set .
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Let us observe that is the “less than” relation on ; is the “greater than “ relation on ; is the “equal to” relation on the set . More formally, we can define: Since the empty set is a subset of , then is a relation on , and we call this the Empty relation . Since is a subset of , then it is also a relation on . This is called the Universal relation on .
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Operations on binary relations Definition . Let be a relation on a set . The inverse of , denoted by , is defined by .
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