a) Let X and Y be sets. Show that X = Y whenever P(X)= P(Y). b)...

 

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a) Let X and Y be sets. Show that X = Y whenever P(X)= P(Y). b) Let f:AB be a function and RC Bx B be an equivalence relation on B. Prove that the relation Q defined by Q:= {(a, a2) € Ax A| (S(a). f(a2) e R} is an equivalence relation on A. e) On the set R of real numbers, determine whether the relation R:= {(* +1. 2)| z€ R} is a funetion from R to R or not. [5,6,4] Question 3. a) Let f: XY and g: Y Z be functions. Show that f is surjective if gof: x- Z is surjective and g is injective. b) Let R be an equivalence relation on X. i) For z€ X, give a description of the equivalence class of z under R, usually denoted by i) Show that the set 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 X and Y be sets. Show that X = Y whenever P(X)= P(Y). b) Let f:AB be a function and RC Bx B be an equivalence relation on B. Prove that the relation Q defined by Q:= {(a, a2) € Ax A| (S(a). f(a2) e R} is an equivalence relation on A. e) On the set R of real numbers, determine whether the relation R:= {(* +1. 2)| z€ R} is a funetion from R to R or not. [5,6,4] Question 3. a) Let f: XY and g: Y Z be functions. Show that f is surjective if gof: x- Z is surjective and g is injective. b) Let R be an equivalence relation on X. i) For z€ X, give a description of the equivalence class of z under R, usually denoted by i) Show that the set 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|

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a If X and Y are sets then PX and PY are the power sets of X and Y respectively Given PXPY So any el... View the full answer