(a) Minimise the following logic function using the Karnaugh maps method: f(a,b,c)=ab+bc+bc+abc (b) Given the following logical circuit with three inputs A,B and C : i. Use the boolean algebra notation and write down the boolean expression of the output, Q of this circuit. [4] ii. Simplify the logical expression in (i). Explain your answer. [5] (c) Let f be a function R{3}R{1} with f(x)=x+3x. i. Show that f is a bijective function [4] ii. Find the inverse function f1 [2] iii. Plot the curves of both function f and f1 on the same graph. [2] iv. suppose we change the co-domain of the function f to be R : f:R{3}R v. Is f still a bijective function? Explain your answer. [3] (d) How many binary sequences of length 8 start with a 1 and end with a 0