Logic Worksheet With Answers Page 5
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22The connective or can mean two different things. Consider the statement “I visited New York
City or Houston, TX.”
This statement can mean (exclusive or) “I visited New York City or Houston, TX but not both.”
It can also mean (inclusive or) “I visited New York City or Houston, TX or both.”
Disjunction is a compound statement formed using the inclusive or represented by the symbol
.
Thus, “p or q or both” is symbolized by p q.
Ex: Let p and q represent the following simple statements:
p: The student prepared for the Test.
q: The student passed the Test.
The statement “The student prepared for the Test or the student passed the Test” can be written
as “p
q”.
The statement “The student prepared for the Test or the student did not pass the Test” can be
written as “p
~q”.
The compound statement “If p, then q is symbolized by p q. This is called a conditional
statement. The statement before the is called the antecedent. The statement after the is
called the consequent.
Ex: This diagram shows a relationship that can be expressed 3 ways:
All men are mortal.
There are no men that are not mortal.
Mortals
If a person is a men, then that person is mortal.
Men
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