Week 7

Venn diagram

Statements:

A statement is a declarative sentence that can be objectively determined to be either true or false, but not both.

A statement does not require an opinion to determine its truth value.

Questions, commands, and exclamations are not statements.

Simple and Compound Statements:

Statements can be classified as simple or compound. A simple statement contains only one idea. Each of these statements is an example of a simple statement.

A compound statement is a statement formed by joining two or more simple statements with a connective.

There are four basic connectives used in logic:

and (the conjunction), or (disjunction),

if . . . then (conditional), and if and only if (biconditional)

Here are some examples of compound statements using connectives.

John studied for 5 hours, and he got an A. (conjunction)

I’m going to pass this class or I’m going to change my major. (disjunction)

If I get 80% of the questions on the LSAT right, then I will get into law school. (conditional)

We will win the game if and only if we score more points than the other team. (biconditional)

Quantified Statements :

Quantified statements involve terms such as all, each, every, no, none, some, there exists, and at least one. The first five (all, each, every, no, none) are called universal quantifiers because they either include or exclude every element of the universal set.

The latter three (some, there exists, at least one) are called existential quantifiers because they claim the existence of something, but don’t include the entire universal set.

Examples of quantified statements:

Every student taking philosophy this semester will pass.
No nursing student is also majoring in criminal justice.
Some people who are Miami Hurricane fans are also Miami Dolphin fans.
There is at least one professor in this school who does not have brown eyes.

Negation:

The negation of a statement is a corresponding statement with the opposite truth value. This means that if a statement is true its negation is false, and if a statement is false its negation is true. For example, for the statement “My dorm room is blue,” the negation is “My dorm room is not blue.” It’s important to note that the truth values of these two are completely opposite: one is true, and the other is false—period.

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