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Thus, the contrapositive of the statement if you live in New York City, then you will live in New York State is if you do not live in New York State, then you do not live in New York City. Note that both statements are true.

1: 2:



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In a merchandising business, inventory is merchan dise that is held for resale. As such, it will ordinar ily be converted into cash in less than a year and is thus a current asset. In a manufacturing business, there will usually be inventories of raw materials and goods in process in addition to an inventory of nished goods. Since we have discussed the Merchandise Inventory ac count as it relates to the worksheet, let us now examine how the mer chandise inventory amount is calculated.

A statement is considered false if one false instance of the statement exists. The converse of a definition is true.

Thus, the definition a quadrilateral is a four-sided polygon and its converse a four-sided polygon is a quadrilateral are both true.

The statement vertical angles are congruent angles is true, but its converse, congruent angles are vertical angles is not necessarily true.





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The statement a square is a quadrilateral is true, but its inverse, a non-square is not a quadrilateral, is not necessarily true.

The contrapositive of a true statement is true, and the contrapositive of a false statement is false.

The statement a triangle is a square is false, and its contrapositive, a non-square is not a triangle, is also false. The statement right angles are congruent angles is true, and its contrapositive, angles that are not congruent are not right angles, is also true.

Logically equivalent statements are pairs of related statements that are either both true or both false. Thus according to Principle 5, a statement and its contrapositive are logically equivalent statements. Also, the converse and inverse of a statement are logically equivalent, since each is the contrapositive of the other. The relationships among a statement and its inverse, converse, and contrapositive are summed up in the rectangle of logical equivalency in Fig. 14-3:

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Under the periodic method, inventory is physically counted at regular in tervals (annually, quarterly, or monthly). When this system is used, cred its are made to the Inventory account or to Purchases, not as each sale is made, but rather in total at the end of the accounting period. To approach the problem of inventory measurement, in order to as sign the business cost to each item, three methods of valuation (FIFO, LIFO, and weighted average) have been developed and approved by GAAP (Generally Accepted Accounting Practices). To compare these three methods, the following data will be used in all of the following in ventory examples. Date Type 1/1 Inventory 3/10 Purchase 6/6 Purchase 10/4 Purchase Available for sale Units 100 150 200 250 700 Unit Cost $6 8 9 10 Totals $ 600 1,200 1,800 2,500 $6,100

Fig. 14-3

1. Logically equivalent statements are at diagonally opposite vertices. Thus, the logically equivalent pairs of statements are (a) a statement and its contrapositive, and (b) the inverse and converse of the same statement. 2. Statements that are not logically equivalent are at adjacent vertices. Thus, pairs of statements that are not logically equivalent are (a) a statement and its inverse, (b) a statement and its converse, (c) the converse and contrapositive of the same statement, and (d) the inverse and contrapositive of the same statement.

Converse of a statement State the converse of each of the following statements, and indicate whether or not it is true. (a) Supplementary angles are two angles the sum of whose measures is 180 . (b) A square is a parallelogram with a right angle. (c) A regular polygon is an equilateral and equiangular polygon.

Using Figure 6-7, identify the following using the node letter codes. 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 Child of ccc. Descendants of ccc. Parent of ccc. Ancestors of ccc. Siblings of ccc. Following sibling of ccc. Preceding sibling of ccc. Following of ccc. Preceding of ccc. Self of ccc. Descendant or self of ccc. Ancestor or self of ccc.

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