Brief presentation on the basic definitions used in Symbolic Logic. This vocabulary uses the first concepts applied at the beginning of a Symbolic Logic course.

1. INTRODUCTIONTO
SYMBOLIC LOGIC
Objective:
• To build up the vocabulary used in symbolic logic.
• To apply the new concepts in particular situations.

3. 1. 1 BASIC DEFINITIONS
The purpose of logic is that, by using or following
certain reasonable thinking, you may reach to valid
conclusions to a specific situation.
Logic can be “the science that deals with the rules
and tests of thinking and proof by reasoning.”
Therefore, Symbolic logic consists on establishing
an artificial symbolic language that can be
applied to simplify complicated logical
arguments.

4. 1.1 BASIC DEFINITIONS
How can we become more logical beings?
We pretend to apply logic not only to the
ordinary mathematical or scientific work, but
to ordinary life also.
In order to communicate in a more intelligent
way with the rest of the people; we need to
acquire the ability to analyze the arguments
presented to us by anyone.

5. 1. 1 BASIC DEFINITIONS
• It is important that we define certain concepts that we
may use throughout this unit:
• Expression: any combination of symbols or a symbol all
by itself. Some examples of expressions are:
𝑎. 𝑥𝑦 𝑏. 5𝑥𝑦 𝑐. + 𝑑. ÷
• Formula: we identify a formula as the equality of two
expressions. Some examples of a formula can be:
𝑎. 3 + 8 = 11 𝑏. 7 − 3 = 4
𝑐. 𝐻𝑜𝑛𝑑𝑢𝑟𝑎𝑠 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑖𝑜𝑛 𝑓𝑢𝑙𝑙 𝑜𝑓 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠.

6. 1.1 BASIC DEFINITIONS
Variable: is a symbol that appears as the subject of
a sentence and that can be replaced for any
element from a universal set.Variables are
commonly written using lower-case letters (x, y, or
z). Some examples of variables are:
x discovered Central America in the 1500’s.
y is an Honduran president from the XX century.
z are the colors in the rainbow.

7. 1.1 BASIC DEFINITIONS
Constant: is a fixed element in a given set. We usually
think of constant values only as numbers, but in terms of
symbolic logic, any element in a set is a constant.
• For example: the set of the vowels is formed by the
constants a, e, i, o, and u.
• Another example can be:The set of the even numbers
between 1 and 11 are the constants 2, 4, 6, 8, and 10.