Let X be the set of all nonempty subsets of {1,2,3}. Then X= {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} Define a relation R on X as follows: For every A and B in X ARB <=> the least element of A equals the least element of B. a, is {1}R{1,2}? is {2}R{3}? is{1,2,3}R{1,3}? is{2,3}R{1,2,3}? b, Prove that R is an equivalence relation on X. and prove R is reflexive, symmetric and transitive.
Let X be the set of all nonempty subsets of {1,2,3}. Then X= {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} Define a relation R on X as follows: For every A and B in X ARB <=> the least element of A equals the least element of B. a, is {1}R{1,2}? is {2}R{3}? is{1,2,3}R{1,3}? is{2,3}R{1,2,3}? b, Prove that R is an equivalence relation on X. and prove R is reflexive, symmetric and transitive.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...
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Let X be the set of all nonempty subsets of {1,2,3}. Then
X= {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
Define a relation R on X as follows: For every A and B in X
ARB <=> the least element of A equals the least element of B.
a, is {1}R{1,2}? is {2}R{3}? is{1,2,3}R{1,3}? is{2,3}R{1,2,3}?
b, Prove that R is an equivalence relation on X. and prove R is reflexive, symmetric and transitive.
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