Handout #8
CS103
April 4, 2011
Robert Plummer
Problem Set #2—Due Monday, April 11 in class
Some problems are from Rosen, and if so, the problem numbers are given.
Reading the answers to similar
oddnumbered problems in the back of the book can provide useful hints.
If a statement/reason proof is
requested, your style should be similar to Example 6, p.67 of Rosen, except all hypotheses should be given
at the beginning and they should be separated from the rest of the proof by a horizontal line.
Note: if you
work with someone else, you are required to (1) write up your answers individually, and (2) indicate
at the top of your paper who was in your group.
Don't forget to put your own name on your paper!
1. (Exercise 6, p. 72)
Use rules of inference to show that the hypotheses “If it does not rain or if it is not
foggy, then the sailing race will be held and the lifesaving demonstration will go on,” “If the sailing race is
held, then the trophy will be awarded,” and “The trophy was not awarded” imply the conclusion “It
rained.”
Use the following symbols:
R = "It rains"
S = "The sailing race will be held"
G = "It is foggy"
L = "The lifesaving demonstration will go on"
2. Give a statement/reason proof for the following. Use a horizontal line to separate hypotheses from the
rest of the proof, as shown.
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 Spring '11
 PLUMMER
 Logic, Rational number, statement/reason proof

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