a) Let f : X Y and g : Y Z be functions. Show that...

 

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a) Let f : X Y and g : Y → Z be functions. Show that f is surjective if go f: X → Z is surjective and g is injective. b) Let R be an equivalence relation on X. i) For x E X, give a description of the equivalence class of r under R, usually denoted by [æ]R• ii) Show that the set II := {{c]R| x € X} of all equivalence classes under R, is a partition on X. (Clearly verify all the conditions for a set to be partition). [6,3,6] a) Let f : X Y and g : Y → Z be functions. Show that f is surjective if go f: X → Z is surjective and g is injective. b) Let R be an equivalence relation on X. i) For x E X, give a description of the equivalence class of r under R, usually denoted by [æ]R• ii) Show that the set II := {{c]R| x € X} of all equivalence classes under R, is a partition on X. (Clearly verify all the conditions for a set to be partition). [6,3,6]