Essay on Accunting Texts and Cases

1353 Words Jan 23rd, 2012 6 Pages
Rosen, Discrete Mathematics and Its Applications, 6th edition
Extra Examples
Section 1.5—Rules of Inference
— Page references correspond to locations of Extra Examples icons in the textbook.
p.67, icon at Example 6
#1. The proposition (￢q ∧ (p → q)) → ￢p is a tautology, as the reader can check. It is the basis for the rule of inference modus tollens:
￢q
p → q
...￢p
Suppose we are given the propositions: “If the class finishes Chapter 2, then they have a quiz” and “The class does not have a quiz.” Find a conclusion that can be drawn using modus tollens.
Solution:
Let p represent “The class finishes Chapter 2” and q represent “The class has a quiz.” According to modus tollens, because we have ￢q and p → q, we can conclude ￢p,
Therefore, the argument is not valid.
p.67, icon at Example 6
#5. Determine whether this argument is valid:
Lynn works part time or full time.
If Lynn does not play on the team, then she does not work part time.
If Lynn plays on the team, she is busy.
Lynn does not work full time.
Therefore, Lynn is busy.
2
Solution:
Using the variables: p: Lynn works part time f: Lynn works full time t: Lynn plays on the team b: Lynn is busy, the argument can be written in symbols: p ∨ f
￢t →￢p t → b
￢f
...b
One method to find whether the argument is valid is to construct the truth table: p f t b p ∨ f ￢t→￢p t→b ￢f b
T T T T T T T F T
T T T F T T F F F
T T F T T F T F T
T T F F T F T F F
T F T T T T T T T
T F T F T T F T F
T F F T T F T T T
T F F F T F T T F
F T T T T T T F T
F T T F T T F F F
F T F T T T T F T
F T F F T T T F F
F F T T F T T T T
F F T F F T F T F
F F F T F T T T T
F F F F F T T T F
We need to examine all cases where the hypotheses (columns 5, 6, 7, 8) are all true. There is only one case in which all four

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