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ssrs barcode font free Improvement of Reasoning in ObjectiveC
CHAPTER 14 Improvement of Reasoning QR Code ISO/IEC18004 Reader In ObjectiveC Using Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications. Painting QR Code In ObjectiveC Using Barcode drawer for iPhone Control to generate, create QRCode image in iPhone applications. 14.3 Converse, Inverse, and Contrapositive of a Statement
QR Code Reader In ObjectiveC Using Barcode decoder for iPhone Control to read, scan read, scan image in iPhone applications. Bar Code Printer In ObjectiveC Using Barcode maker for iPhone Control to generate, create barcode image in iPhone applications. DEFINITION 1: Generate Denso QR Bar Code In Visual C# Using Barcode maker for .NET framework Control to generate, create QR Code image in VS .NET applications. Creating QRCode In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create QR Code image in ASP.NET applications. The converse of a statement is the statement that is formed by interchanging the hypothesis and conclusion. Quick Response Code Encoder In Visual Studio .NET Using Barcode encoder for .NET framework Control to generate, create QR Code image in .NET framework applications. Print Quick Response Code In Visual Basic .NET Using Barcode drawer for .NET framework Control to generate, create QR image in Visual Studio .NET applications. Thus, the converse of the statement lions are wild animals is wild animals are lions. Note that the converse is not necessarily true. Printing Barcode In ObjectiveC Using Barcode drawer for iPhone Control to generate, create barcode image in iPhone applications. Creating ANSI/AIM Code 128 In ObjectiveC Using Barcode drawer for iPhone Control to generate, create Code 128B image in iPhone applications. DEFINITION 2: USS128 Generator In ObjectiveC Using Barcode printer for iPhone Control to generate, create GTIN  128 image in iPhone applications. Creating Code39 In ObjectiveC Using Barcode drawer for iPhone Control to generate, create USS Code 39 image in iPhone applications. The negative of a statement is the denial of the statement.
GS1  12 Printer In ObjectiveC Using Barcode generator for iPhone Control to generate, create UPCE Supplement 5 image in iPhone applications. Reading Barcode In Visual C# Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications. Thus, the negative of the statement a burglar is a criminal is a burglar is not a criminal.
Generating Code39 In Java Using Barcode creator for Java Control to generate, create Code 39 Full ASCII image in Java applications. GS1  12 Decoder In .NET Framework Using Barcode recognizer for VS .NET Control to read, scan read, scan image in VS .NET applications. DEFINITION 3: Painting EAN / UCC  13 In None Using Barcode drawer for Online Control to generate, create GTIN  13 image in Online applications. Painting Code39 In .NET Using Barcode creator for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications. The inverse of a statement is formed by denying both the hypothesis and the conclusion.
Code128 Generator In None Using Barcode drawer for Office Word Control to generate, create Code 128 Code Set A image in Word applications. Barcode Creation In .NET Using Barcode generation for Visual Studio .NET Control to generate, create bar code image in VS .NET applications. Thus, the inverse of the statement a burglar is a criminal is a person who is not a burglar is not a criminal. Note that the inverse is not necessarily true. DEFINITION 4: The contrapositive of a statement is formed by interchanging the negative of the hypothesis with the negative of the conclusion. Hence, the contrapositive is the converse of the inverse and the inverse of the converse. 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. 14.3A Converse, Inverse, and Contrapositive Principles
PRINCIPLE PRINCIPLE
1: 2: 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 foursided polygon and its converse a foursided polygon is a quadrilateral are both true. PRINCIPLE
The converse of a true statement other than a definition is not necessarily true.
The statement vertical angles are congruent angles is true, but its converse, congruent angles are vertical angles is not necessarily true. PRINCIPLE
The inverse of a true statement is not necessarily true.
The statement a square is a quadrilateral is true, but its inverse, a nonsquare is not a quadrilateral, is not necessarily true. PRINCIPLE
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 nonsquare 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. 14.3B Logically Equivalent Statements
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. 143: CHAPTER 14 Improvement of Reasoning
Fig. 143 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. SOLVED PROBLEMS
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. Solutions
(a) Two angles the sum of whose measures is 180 are supplementary. (True) (b) A parallelogram with a right angle is a square. (False) (c) An equilateral and equiangular polygon is a regular polygon. (True) Negative of a statement State the negative of (a) a b; (b) m B m C; (c) does not lie on the line.
Solutions
(a) a b (b) m B (c) m C D.
C is the complement of
D; (d) the point
C is not the complement of
(d) The point lies on the line.
Inverse of a statement State the inverse of each of the following statements, and indicate whether or not it is true. (a) A person born in the United States is a citizen of the United States. (b) A sculptor is a talented person. (c) A triangle is a polygon.

