hw2solutions

Hw2solutions - disjunctions by using NAND’s Thus every compound proposition can be converted into a logically equivalent compound proposition

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SOLUTIONS TO HOMEWORK #2 Total point : 80 Section 1.2: 29, 32, 52, 54 (Each sum carry 5 points) 29 . Solution is provided at the back of the textbook. 32 . We just need to find an assignment of truth values that makes one of these propositions true and the other false. We can let p be true and the other two variables false. Then the first statement will be F ՜ F, which is true, but the second will be F ٿ T, which is false. 52 . From the truth tables that, (p | p) ؠ ( p) and that [(p | p) | (q | q)] ؠ ሺ pVq). Then we can argue that every compound proposition is logically equivalent to one that uses only and V. but by our observations at the beginning of the p[resent exercise, we can get rid of all the negations and
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Unformatted text preview: disjunctions by using NAND’s. Thus every compound proposition can be converted into a logically equivalent compound proposition involving only NAND’s. 54 . To show that these are not logically equivalent, we need to fing only one assignment of thruth values to p, q, and r for which the truth values of p|(q|r) and (p|q)|r differ. One such assignment is T for p and F for q and r. then computing from the truth tables (of definitions), we see thet p|(q|r) is false and (p|q)|r is true. Section 1.3: 10, 40, 56, 62 (Each sum carry 5 points) Section 1.4: 26, 28, 30, 40 (Each sum carry 5 points) Section 1.5: 4, 12, 14, 30 (Each sum carry 5 points)...
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Hw2solutions - disjunctions by using NAND’s Thus every compound proposition can be converted into a logically equivalent compound proposition

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