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A large portion of all business transactions are cred it transactions. One way of extending credit is by the acceptance of a promissory note, a contract in which one person (the maker) promises to pay another per

s (a) Since AB and AC are straight lines, j a and j b are straight j. Hence, j a > j b. are congruent.

s (b) Since BA ' AD and BC ' CD, j a and j b are rt. j. Hence, j a > j b. Ans. All right angles are congruent.



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(c) Since AB ' BC, j B is a rt. j , making j b the complement of j 1. Since j a is the complement of j 1, j a > j b. Ans. Complements of the same angle are congruent.

The statements A heated metal expands and If a metal is heated, then it expands are two forms of the same idea. The following table shows how each form may be divided into its two important parts, the hypothesis, which tells what is given, and the conclusion, which tells what is to be proved. Note that in the if-then form, the word then may be omitted. Hypothesis (What is given) Hypothesis is subject: A heated metal Hypothesis is if clause: If a metal is heated Conclusion (What is to be proved) Conclusion is predicate: expands Conclusion is then clause: then is expands





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Form Subject-predicate form: A heated metal expands. If-then form: If a metal is heated, then it expands.

The converse of a statement is formed by interchanging the hypothesis and conclusion. Hence to form the converse of an if-then statement, interchange the if and then clauses. In the case of the subject-predicate form, interchange the subject and the predicate. Thus, the converse of triangles are polygons is polygons are triangles. Also, the converse of if a metal is heated, then it expands is if a metal expands, then it is heated. Note in each of these cases that the statement is true but its converse need not necessarily be true.

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Any XML document is part of a set of XML documents that are logically equivalent within an application context, but which vary in physical representation based on syntactic changes permitted by XML 1.0 and Namespaces in XML. This speci cation describes a method for generating a physical representation the canonical form of an XML document that accounts for the permissible changes. Except for limitations regarding a few unusual cases, if two documents have the same canonical form, then the two documents are logically equivalent within the given application context. Note that two documents may have di ering canonical forms yet still be equivalent in a given context based on application-speci c equivalence rules for which no generalized XML speci cation could account.

PRINCIPLE 1:

son (the payee) a speci c sum of money at a speci c time, with or with out interest. A promissory note is used for the following reasons: 1. The holder of a note can usually obtain money by taking the note to the bank and selling it (discounting the note). 2. The note is a written agreement of a debt and is better evidence than an open account. 3. The note facilitates the sale of merchandise on long-term or in stallment plans. For a note to be negotiable, it must meet the requirements of the Uni form Negotiable Instrument Law. This legislation states that the instru ment: 1. The note must be in writing and signed by the maker. 2. The note must contain an order to pay a de nite sum of money. 3. The note must be payable to order on demand or at a xed future time.

The converse of a true statement is not necessarily true. The converse of a definition is always true.

PRINCIPLE 2:

Thus, the converse of the definition a triangle is a polygon of three sides is a polygon of three sides is a triangle. Both the definition and its converse are true.

2.11 Determining the hypothesis and conclusion in subject-predicate form Determine the hypothesis and conclusion of each statement. Solutions Hypothesis (subject) Perpendiculars Complements of the same angle An equilateral triangle A right triangle A triangle

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