A set is an unordered collection of objects.
The objects in a set are called the elements, or members, of the set. A set is
said to contain its elements.
1.7 Introduction to Proofs
Formal proofs of theorems designed for human consumption are almost always informal
proofs, where more than one rule of inference may be used in each step, where steps
1.6 Rules of Inference
A sequence of statements that ends with a conclusion.
The conclusion, or final statement of the argument, must follow from the truth
of the prece
1.1 Propositional Logic
A proposition is a declarative sentence that is either true or false but not
The following is a declarative sentence.
Washington D.C. is the capital of the Unit
1.2 Applications of Propositional Logic
Translating English Sentences
How can this English sentence be translated into a logical expression?
You can access the Internet from campus only if you are a comput
1. Create file p01.cpp in the root directory of your account for this class on the departmental
2. Enter your author identification block consisting of
2.1. Your name, for example, Mr
1.5 Nested Quantifiers
Express ( + = 0) without the existential quantifier.
Solution: ( + = 0) is the same as () where () is (, )
and (, ) = + = 0
Translate ( > 0) ( < 0) < 0) into E
1.3 Propositional Equivalences
A compound proposition that is always true, no matter what the truth values
of the propositions that occur in it, is called a tautology.
A compound proposition that is alw
1.4 Predicates and Quantifiers
In this section we will introduce a more powerful type of logic called predicate logic.
Consider the statement: > 3. The statement has two parts:
1. the variabl