a) Show that (a, b) := {{a}, {b}} does not satisfy the ordered pair axiom. b)...

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a) Show that (a, b) := {{a}, {b}} does not satisfy the ordered pair axiom. b) Determine whether each of the following statements is true or false. (Give a reason in each case): (i) {a, b} C (a, b). (ii) {{a, b}} C (a, b). c) Prove that Xn (Y\ Z) = (X nY)\Z. (6,2,2,5) Question 2. a) Let X and Y be sets. Show that X Y whenever P(X) = P(Y). b) Let f : A – B be a function and RC Bx B be an equivalence relation on B. Prove %3D that the relation Q defined by Q:= {(a1, a2) E Ax A| (f(a1), f(a2)) E R} is an equivalence relation on A. c) On the set R of real numbers, determine whether the relation R {(x² + 1, x)| x E R} is a function from R to R or not. [5,6,4] a) Show that (a, b) := {{a}, {b}} does not satisfy the ordered pair axiom. b) Determine whether each of the following statements is true or false. (Give a reason in each case): (i) {a, b} C (a, b). (ii) {{a, b}} C (a, b). c) Prove that Xn (Y\ Z) = (X nY)\Z. (6,2,2,5) Question 2. a) Let X and Y be sets. Show that X Y whenever P(X) = P(Y). b) Let f : A – B be a function and RC Bx B be an equivalence relation on B. Prove %3D that the relation Q defined by Q:= {(a1, a2) E Ax A| (f(a1), f(a2)) E R} is an equivalence relation on A. c) On the set R of real numbers, determine whether the relation R {(x² + 1, x)| x E R} is a function from R to R or not. [5,6,4]