CS202: Discrete Structures

1.2: Conditional Statements

• As you have likely noticed there is a similarity between the language of logic and a natural language, such as English. In fact, there is a similarity between implication in logic and the conditional statement in English, i.e. an if statement. In the follow subsections, we will study the application of operations to the logical if statement. 
  

• 1.2.1: Logical Equivalences Using Conditional Statements

  • Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic" URL

    Read Section 1.1.2 and Section 1.1.3 on pages 4 and 5. Section 1.1.3 of this reading also applies to Subunit 1.2.5.

    The conditional statement in English can be translated to implication in logic.

  • University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic" URL

    Read the section titled "Implication" up to the exercises on pages Lo-4 - Lo-9. For the English translation discussion, see example 3 on page Lo-6 and Subunit 1.1.2 of this course. Example 3 also covers the Negation of a Conditional Statement, the Contrapositive of a Conditional Statement, and the Converse and Inverse of a Conditional Statement.
    

• 1.2.2: If and Only If, Necessary and Sufficient Conditions

  • University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic" URL

    Read example 5 on pages Lo-7 - Lo-8. Note that in the statement A if and only if B, abbreviated A iff B, A is called the necessary part and B the sufficient part.
    

• 1.2.3: Proving Validity or Invalidity of an Argument Using Truth Tables

  • Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Logic" URL

    Read Section 1.2 on pages 5 and 6 and 1.4 on pages 6 - 8 to learn about logical equivalence of statements. The term validity refers to an argument or proof. We say an argument is valid if its conclusion logically follows from its premises. We can do this by showing that a statement is logically equivalent to a premise, or by showing that a statement logically follows from a premise. Logically follows from, or is a consequence of, means that the conclusion is true if the premise is true.
    

  • University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Boolean Functions and Computer Arithmetic" URL

    Read example 7 on pages BF-7 and BF-8. This is an example where a given expression is transformed into a logically equivalent expression, which, in turn, is translated into another equivalent express, and so on.
    

  • Validity and Arguments URL

    Read this article.