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11 Nov 2019
help me to solve this problem
Let n be a fixed positive integer and let X Zn be nonempty with the property that [a - b]n epsilon X for all [a]n, [b]n epsilon X. Prove that addition modulo n is an operation on X. (That is, show that X is closed under addition modulo n.) Hint: First prove that [-y]n epsilon X for all [y]n epsilon X. Prove that the relation teta Zn times Zn defined by ([z]n, [y]n) epsilon teta if and only if [x - y]n epsilon X is an equivalence relation. Show that the partition on Zn induced by teta has the form F = {S[a]n : [a]n epsilon Zn}, where S[a]n ={[a + x]n: [x]n epsilon X}.
help me to solve this problem
Let n be a fixed positive integer and let X Zn be nonempty with the property that [a - b]n epsilon X for all [a]n, [b]n epsilon X. Prove that addition modulo n is an operation on X. (That is, show that X is closed under addition modulo n.) Hint: First prove that [-y]n epsilon X for all [y]n epsilon X. Prove that the relation teta Zn times Zn defined by ([z]n, [y]n) epsilon teta if and only if [x - y]n epsilon X is an equivalence relation. Show that the partition on Zn induced by teta has the form F = {S[a]n : [a]n epsilon Zn}, where S[a]n ={[a + x]n: [x]n epsilon X}.
Keith LeannonLv2
12 Oct 2019