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Assignment 1 exercises full document
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(a) Find a proposition with three variables p, q, and r that is true when p and r are true and q is false, and false otherwise. (b) Find a proposition with three variables p, q, and r that is true when at most one of the three variables is true, and false otherwise. (c) Find a proposition with three variables p, q, and r that is never true.
(a) Write a proposition equivalent to p ∨ ¬q that uses only p, q, ¬, and the connective ∧. (b) Write a proposition equivalent to p → q using only p, q, ¬, and the connective ∨.
(a) It is neither cold nor dry. (b) It is rainy if it is not cold. (c) To be windy it is necessary that it be cold. (d) It is rainy only if it is windy and cold.
(a) A says “I am not a knight,” B says “I am not a spy,” and C says “I am not a knave.” (b) A says “I am a spy,” B says “I am a spy” and C says “B is a spy.”