Determine whether the argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16. For each valid argument, state the name of its standard form.
If I had a nickel for every logic problem I have solved, then I would be rich. I have not received a nickel for every logic problem I have solved. Therefore, I am not rich.
To identify:
Whether the given argument is valid or invalid by comparing its symbolic form with the standard forms given in Tables 3.15 and 3.16 and for each valid argument, state the name of its standard form.
Given information:
If I had a nickel for every logic problem I have solved, then I would be rich. I have not received a nickel for every logic problem I have solved. Therefore, I am not rich.
Concept Involved:
An Argument and a Valid Argument: Anargumentconsists of a set of statements calledpremisesand another statement called theconclusion. An argument isvalidif the conclusion is true whenever all the premises are assumed to be true. An argument isinvalidif it is not a valid argument. A symbolic argument consists of a set of premises and a conclusion. It is called a symbolic argument because we generally write it in symbolic form to determine its validity.
A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by A disjunction is false if and only if both statements are false; otherwise it is true. 
A conjunction is a compound statement formed by joining two statements with the connector AND. The conjunction "p and q" is symbolized by

A conditional statement, symbolized by

A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a doubleheaded arrow The biconditional represents "p if an only if q", where p is a hypothesis and q is a conclusion. 
Standard Forms:
Arguments can be show to be valid if they have the same symbolic form as an argument that is known to be valid. For instance, we have shown that the argument is valid.
This symbolic form is known asdirect reasoning. All arguments that have this symbolic form are valid.
Transitive reasoning can be extended to include more than two conditional premises. For instances, if the conditional premises of an argument are
Table 3.15 shows four symbolic forms and the name used to identify each form. Any argument that has a symbolic form identical to one of these symbolic forms is a valid argument.
Table 3.15 Standard Forms of Four Valid Arguments  
Direct Reasoning  Contrapositive Reasoning  Transitive Reasoning  Disjunctive Reasoning  
Table 3.16 shows to two symbolic forms associated with invalid arguments. Any argument that has one of these symbolic forms is invalid.
Table 3.16 Standard Forms of TWO Invalid Arguments  
Fallacy of the converse  Fallacy of the inverse 
Calculation:
In the argument given, the two premises and the conclusion are shown below
Finite Mathematics
Mathematical Applications for the Management, Life, and Social Sciences
Finite Mathematics and Applied Calculus (MindTap Course List)
Applied Calculus
Understanding Basic Statistics
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals, Volume I
Statistics for The Behavioral Sciences (MindTap Course List)
Multivariable Calculus
Essentials Of Statistics
Calculus: An Applied Approach (MindTap Course List)
Intermediate Algebra
Probability and Statistics for Engineering and the Sciences
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus: Early Transcendental Functions
Single Variable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Elementary Technical Mathematics
Single Variable Calculus: Early Transcendentals
Contemporary Mathematics for Business & Consumers
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Elementary Geometry For College Students, 7e
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendental Functions (MindTap Course List)
Elementary Geometry for College Students
Calculus of a Single Variable
Mathematics For Machine Technology
Mathematics: A Practical Odyssey
College Algebra (MindTap Course List)
Introduction To Statistics And Data Analysis
Calculus (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Study Guide for Stewart's Multivariable Calculus, 8th
Statistics for Business & Economics, Revised (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Multivariable Calculus
STATISTICS F/BUSINESS+ECONOMICSTEXT
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th