GNED 1101 Chapter Notes - Chapter 1.2: Sentence Clause Structure, Material Conditional, If And Only If

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Section 1.2 Compound Statements and Connectives
Compound Statements
Simple Statements each convey one idea with no connecting words (“You’re wealthy”, “You’re well educated”)
Statements that are formed by combining two or more simple statements are called compound statements
o Words called connectives are used to join these simple statements together.
o Connective words include; and, or, if….then, if and only if
And Statements
If two simple statements are connected using the connective “and”, and is symbolically represented by
The compound statement formed by using the word and is called a conjunction
Example Simple Sentences into a compound sentence
o P: It is after 5pm
o Q: They are Working
COMPOUNDED - It is after 5pm and they are working
Symbolically illustrated as p q
o Compounded with Negation
It is after 5pm and they are not working
Symbollically illustrated as p q
The symbol for “and” can also be translated as but, yet, nevertheless
o It is after 5pm and they are working
o It is after 5pm, but they are working
o It is after 5pm, yet they are working
o It is after 5pm, nevertheless they are working
Or Statements
Or as a connective has two meanings
o I visited London or Paris means I visited London or Paris but not both
This is an exclusive or, which means one or the other, but not both
o I visited London or Paris or both
This is an inclusive or, which means either or both
In mathematics, the use of the connective or means the inclusive or. If p and q represent two simple
statements, then the compounded statement “ p or q “ means “p or q or both”.
Or as a connective is called a disjunction and is symbolized by
Thus, the compoundd statement “p or q or both” can by symbolized as p q.
Example
o “The bill receives majority approval or the bill becomes law” can be symbolized as p q
o “The bill receives majority approval or the bill does not become a law” can be symbolized as pq
If-Then Statements
If p, then q
If-then is symbolized by
If-then is thus a conditional statement
In a conditional statement, the statement before the is called the antecedent, and the statement after the
is called the consequent
o Antecedent Consequent
Example:
o P: A person is a father
o Q: A person is a male
A few options:
If a person is a father, then that person is a male is symbolized as pq
If a person is a male, then that person is a father is symbolized as qp
If a person is not a male, then that person is not a father is symbolized as:
q p
If-Then can also be translated differently
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