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Deductive reasoning enables us to derive true or acceptably true conclusions from statements which are true or accepted as true. It consists of three steps as follows: 1. Making a general statement referring to a whole set or class of things, such as the class of dogs: All dogs are quadrupeds (have four feet). 2. Making a particular statement about one or some of the members of the set or class referred to in the general statement: All greyhounds are dogs. 3. Making a deduction that follows logically when the general statement is applied to the particular statement: All greyhounds are quadrupeds. Deductive reasoning is called syllogistic reasoning because the three statements together constitute a syllogism. In a syllogism the general statement is called the major premise, the particular statement is the minor premise, and the deduction is the conclusion. Thus, in the above syllogism: 1. The major premise is: All dogs are quadrupeds. 2. The minor premise is: All greyhounds are dogs. 3. The conclusion is: All greyhounds are quadrupeds. Using a circle, as in Fig. 2-1, to represent each set or class will help you understand the relationships involved in deductive reasoning. 1. Since the major premise or general statement states that all dogs are quadrupeds, the circle representing dogs must be inside that for quadrupeds. 2. Since the minor premise or particular statement states that all greyhounds are dogs, the circle representing greyhounds must be inside that for dogs.



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Fig. 2-1

3. The conclusion is obvious. Since the circle of greyhounds must be inside the circle of quadrupeds, the only possible conclusion is that greyhounds are quadrupeds.

Observation cannot serve as proof. Eyesight, as in the case of a color-blind person, may be defective. Appearances may be misleading. Thus, in each part of Fig. 2-2, AB does not seem to equal CD although it actually does.

Fig. 2-2





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thereby keeping earnings from being greatly distorted by any uctuating increases or de creases in prices. Yet it sometimes allows too much maneuvering by managers to change net income. For example, if prices are rising rapid ly and a company wishes to pay less taxes for that year, management can buy large amounts of inventory near the end of that period. These higher inventory costs, because of prices, under LIFO immediately be come an expense, and thus result in the nancial statement showing a lower net income. Conversely, if the rm is having a bad year, manage ment may want to increase net income to garner favor with stockholders. This can be done by delaying any large purchase of high-cost inventory until the following period by keeping the purchase out of the Cost of Goods Sold section for the current year, and thus avoiding any decrease in net income. In a rising market, certain tax advantages are gained through LIFO because it yields a lower pro t because of its higher cost of goods sold. This can be shown by using the data while assuming sales of $20,000 for the year. FIFO Sales $20,000 Cost of Goods Sold Goods Available for Sale $6,100 3,130 Less: Ending Inventory Cost of Goods Sold 2,970 Gross Pro t $17,030 LIFO $20,000 $6,100 2,430 3,670 $16,330

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Measurement cannot serve as proof. Measurement applies only to the limited number of cases involved. The conclusion it provides is not exact but approximate, depending on the precision of the measuring instrument and the care of the observer. In measurement, allowance should be made for possible error equal to half the smallest unit of measurement used. Thus if an angle is measured to the nearest degree, an allowance of half a degree of error should be made. Experiment cannot serve as proof. Its conclusions are only probable ones. The degree of probability depends on the particular situations or instances examined in the process of experimentation. Thus, it is probable that a pair of dice are loaded if ten successive 7s are rolled with the pair, and the probability is much greater if twenty successive 7s are rolled; however, neither probability is a certainty.

2.1 Using circles to determine group relationships In (a) to (e) each letter, such as A, B, and R, represents a set or group. Complete each statement. Show how circles may be used to represent the sets or groups. (a) If A is B and B is C, then _____ . (b) If A is B and B is E and E is R, then _____ .

(c) If X is Y and _____ , then X is M. (d) If C is D and E is C, then _____ . (e) If squares (S) are rectangles (R) and rectangles are parallelograms (P), then _____ .

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