Answer to Question #210159 in Discrete Mathematics for Kojo

Question

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]

Answer 1

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