The Nature of Mathematics, 12th Edition
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Section 3.3: Operators and Laws of Logic

3.3 Outline

A. Biconditional, implication, and logical equivalence
     1. definition of biconditional
     2. verifying tautologies
     3. implication
     4. equivalence
B. Laws of logic
     1. law of double negation
     2. law of contraposition
     3. De Morgan's laws
C. Negation of a compound statement
     1. negation of a conditional
     2. language analysis
D. Miscellaneous operators
     1. either p or q
     2. neither p nor q
     3. p unless q
     4. p because q
     5. no p is q

3.3 Essential Ideas

The biconditional tests to see if two statements have the same truth values. The formal definition is given here:

Additional operators:

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