15) Let A = {7,9,10,12}, B = {1,2,3,4} and consider the relations:

R = {(a,b)AB | a-2b 3}

G = {(a,b) | aA , bB and (a+b) = 12}

H = {(a,b) | aB , bB and (a+b) > 5}

(a) List all the elements of the relation R and give its cardinality |R|. (4 marks)

(b) Find the range and domain of the relation R. (2 marks)

(c) Find the inverse relation R-1. (2 marks)

(d) Find the sets of ordered pair in G and H. (6 marks)

(e) Draw the diagraphs of G and H. (6 marks)

(f) Give the Boolean-matrix representations of G and H. (2 marks)

16) Determine whether each of these functions is a bijection from to , where is the set

of real numbers, justify your answers: (6 marks)

(a) f(x)=2x+1

(b) f(x)=x2 +1

(c) f(x)=x3