1. [9 marks] Representation of numbers and round-off errors (a) Decide if the following equations are mathematically correct. Then implement them in mat- lab. For each equation, interpret if the result in matlab is consistent with the mathematical equation. Explain any deviation. (For example, the equation 3 +7 5 in matlab would correspond to the command disp (3+7 25) and yields, upon execution of the command, the value 0 corresponding to false. This is expected since the equation is not true.) o 1000 1/1000 1000 101/101- 10 15 3+10-1 3 10-17 . 423252 . 12 +82 12+8 (b) Write a MATLAB program that creates a vector i-0:64 and a corresponding vector x with values 20,21,22,264. Then, for each element in x, calculate y- (-3*x+1)+(1+3*x) and store the result in a vector y. Plot y as a function of i (not y as a function of x!). Explain the result and the differences to the expected value 2. [6 marks] Use Venn diagrams to test which of the following statements are generally true for arbitrary sets A, B and C. Your drawings must explain, how you constructed the Venn diagrams for the right-hand side and the left-hand side of the equations (e.g. by showing intermediate steps). You need to state clearly if the relationship is true or false 1. [9 marks] Representation of numbers and round-off errors (a) Decide if the following equations are mathematically correct. Then implement them in mat- lab. For each equation, interpret if the result in matlab is consistent with the mathematical equation. Explain any deviation. (For example, the equation 3 +7 5 in matlab would correspond to the command disp (3+7 25) and yields, upon execution of the command, the value 0 corresponding to false. This is expected since the equation is not true.) o 1000 1/1000 1000 101/101- 10 15 3+10-1 3 10-17 . 423252 . 12 +82 12+8 (b) Write a MATLAB program that creates a vector i-0:64 and a corresponding vector x with values 20,21,22,264. Then, for each element in x, calculate y- (-3*x+1)+(1+3*x) and store the result in a vector y. Plot y as a function of i (not y as a function of x!). Explain the result and the differences to the expected value 2. [6 marks] Use Venn diagrams to test which of the following statements are generally true for arbitrary sets A, B and C. Your drawings must explain, how you constructed the Venn diagrams for the right-hand side and the left-hand side of the equations (e.g. by showing intermediate steps). You need to state clearly if the relationship is true or false