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Answer All Questions QUESTION 1 (20 Marks) (a) (b) (c) (e) Determine whether each of the statements below is true or false. (i) 100 is the smallest 3-digit hexadecimal number, and 999 is the largest 3-digit hexadecimal number. (ii) Number 1 is rational if and only if all integers are rational. Rewrite the statement below in if-then form. This loop will repeat exactly N times if it does not contain a stop or a go to. Write the negation for each of the statements below. (i) (ii) Final Exam (i) (d) Let p, q and r be the propositions below: p: DATAENDFLAG is off. q: ERROR equals -1. r: PRODUCT is greater than 50 Express the following sentences in symbolic notation. (A) (ii) Eric found at least 3 errors in the system within a week. (B) (1 mark) If Lynn is wise, then she is brilliant in doing research. (Hint: Given p→→q=~pvq, use De Morgan's law to write the negation of the statement.) (2 marks) 50. Page 1 of 6 (2 marks) DATAENDFLAG is off, ERROR equals -1, and PRODUCT is greater than Express the compound propositions below as an English sentence. p<(~qv~r) (2 marks) Show that the compound proposition below is indeterminant using truth table. ~(rp) → (pv~qvr) (2 marks) Either DATAENDFLAG is on, or it is the case that both ERROR equals -1 and PRODUCT is greater than 50. (3 marks) (3 marks) (5 marks)
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