7:14 I. II. Let X = {a,b, c, d, e} and Y = { 10, 11, 12}. a) How many functions are there from set X to set Y? b) Write all functions from set X to set Y. *You can write functions using arrow diagrams, order pairs form, or in image form. III. IV. V. VI. Any submission will not be entertained after the submission deadline. 16 KB/s Questions: [Total Marks: 100] [CO 1, SO 2] VII. Let A = {5, 6, 7, 8, 9, 10} and B = {7, 8, 9, 10, 11, 13). Define a relation R from A to B by R = {(a, b) A x B | b = a +2} [10] a) Write down the Domain and Range of R. b) Draw an Arrow Diagram for the relation R. c) Represent the relation R using Matrix. Let A = {a, b} and B = {1, 2, 3). Find A B, B x A, A A, and B x B. How many elements will be in each cartesian product? [15] Let f: NN: f(x) = 2x for all x in N. Check whether f is a bijection. + 76% Let A = {1, 2} and B = {3, 6} and f and g be functions from A to B, defined by f(x) = 3x and g(x) = x + 2. Show that f = g. [15] Page 1 of 2 HITEC UNIVERSITY Taxila Department of Computer Science [15] a) What is the cost function? b) What is the revenue function? c) What is the profit function? d) How much is the profit when 500 units of purses are sold? [15] An electrician charges a base fee of $70 plus $50 for each hour of work. Create a table that shows the amount the electrician charges for 1,2,3, and 4 hours of work. Let x represent the number of hours and y represent the amount charged for x hours. Is this a relation or function? [15] A Company produces and sells purses. The daily operating expenses of the company in producing purse is Rs. 6000 and the cost is Rs. 30 per unit. The company sells the product at Rs. 60 per unit. [15]