# hmk1 - COT 3100 Homework#1 Fall 2000 Section 2 Lecturer...

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COT 3100 Homework #1 Fall 2000 Section 2 Lecturer: Arup Guha Assigned: 8/29/00 Due: 9/7/00 1) Fill out a truth table to evaluate which truth assignments make the expression ¬ p ( ¬ (q r)) true. 2) Use the truth table method to verify that ( ¬ q ¬ p) ((p q) r)) is logically equivalent to the expression r p. (Notice that you must have a column for q in your truth table for p r, even though q is not part of the expression in order to evaluated the equivalence.) 3) Use only the laws of logic on page 59 of the text to show the equivalence of the two expressions in question 2. (You may also use the implication identity: p q is logically equivalent to ¬ p q.) Show each step and note the law used at each step. 4) Write the following arguments in symbolic form. (Assign p, q, r, etc. to simple statements and then translate the argument into multiple complex statements using p, q and r...) Then establish the validity of the argument or give a counterexample to show that it is invalid.

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