Answer to Question #179903 in Discrete Mathematics for Johnson

Question #179903

Let R be a relation from the set A to the set B, then: Prove that Ran (R)=Dom (R-1 ). 


1
Expert's answer
2021-04-13T13:45:53-0400

Let "R" be a relation from the set "A" to the set "B". Taking into account that "R^{-1}=\\{(b,a)\\ |\\ (a,b)\\in R\\}\\subset B\\times A", we conclude that "Ran (R)=\\{b\\ |\\ (a,b)\\in R\\}=\\{b\\ |\\ (b,a)\\in R^{-1}\\}=Dom (R^{-1} )."


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