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Midterm

# Solutions to ch1 for test 1 (30%).

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University of Toronto St. George

Philosophy

PHL246H1

Colin Howson

Winter

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Exercise Answers. Chapter One. 1. i. For the truth table, go to http:turner.faculty.swau.edumathematicsmaterialslibrarytruth and type in ~(A&(B+~C)) for the Boolean expression and hit generate table. ii. A truth table will have 2 to the power of X rows, where X is the number of lettersvariables you are using. In this case, it is 2^5=32 rows. 2. i. For this truth table, go to the same website as above and paste in A&(B+C) as the left side, and (A&B)+(A&C) for the right side. ii. Use the site again, with A+(B&C) for the table for the left side of the equation, and (A+B)&(A+C) for the right. 3. i. If B1,B2,,Bn are mutually exclusive, then only one of them can be true at one point in time. Now, in a conjunction (eg A^B1), if any term is false, then the whole conjunction is false. So, if only one of B1 through Bn can be true at any point in time, then all but one are false at the point in time. It follows then that all but one

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