Question 1. [20 Marks] a) Let p, q, and r be the propositions: p = "the flag is set" q = "I = 0" r = "subroutine S is completed" Translate each of the following propositions into symbols, using the letters p, q, r and logical connectives. (i) If the flag is set, then I = 0 [2 marks] (ii) The flag is set and I = 0 if subroutine S is not completed [2 marks] (iii) Subroutine S is completed if and only if I = 0 and flag is set [2 marks] b) State the converse, contrapositive, and inverse of each of these conditional statements. (i) If it snows tonight, then I will stay at home [3 marks] (ii) I go to the beach whenever it is a sunny summer day [3 marks] (iii) When I stay up late, it is necessary that I sleep until noon [3 marks] c) Explain the step-by-step procedure involved in finding the inverse of an n by n square matrix. [5 marks]
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