Discrete Math / Truth Tables

Discrete Math is a concentration of math that focuses on the distinct fundamental properties of math and statements. At a basic level, it is categorizing a statement as either a part of one system or another.

In this case, we will be using truth tables to help visualize this process.

I will go over 4 statements in discrete math:

The “and”, “or”, “exclusive or”, and “implies” statements.

“And” - ∧

The “and” (∧) statement means the combination of both statements has to be true for it to be true, if not it is false.

For example:

A Statement	B Statement	A ∧ B Statement
T	F	F (This statement is False)

Moving on to another statement,

“Or” - V

The “or” (V) statement means that the combination of both statements is true when one of the statements is true.

For example:

A Statement	B Statement	A V B Statement
T	T	T (This statement is True)
T	F	T (This statement is True)
F	T	T (This statement is True)

Moving on to another statement,

“Exclusive Or” - ⊕

The “exclusive or” (⊕) statement means that the combination of both statements is true when ONLY ONE of the statements is true. If both of the statements are true, or both of the statements are false then the combination is false.

For example:

A Statement	B Statement	A ⊕ B Statement
T	T	F (This statement is False)
T	F	F (This statement is True)
F	F	F (This statement is False)

Moving on to the last statement,

“Implies” - →

The “implies” (→) statement means that the combination of the statements is false if a false statement implies a true statement, otherwise, the combination of the statements is true. True can not imply false.

For example:

A Statement	B Statement	A → B Statement
T	T	T (This statement is True)

Now go and solve those truth tables!