Conditional Propositions in Propositional Logic

Conditional Propositions in Propositional Logic



Conditional propositions are compound propositions connected by the words
“If…then” or just “then.” Please note that the symbol for “if…then” is a horseshoe.

Consider the example below:

If it rains today, then the road is wet. (p, q)

If we let p stand for “It rains today” and q for “The road is wet,” then the example above
is symbolized as follows:

p⊃q

Please note that the proposition that precedes the connective horseshoe (⊃) is called
the “antecedent” and the proposition that comes after it is called “consequent.”

Please note as well that there are cases wherein the words “if…then” is not mentioned
in the proposition, yet the proposition remains a conditional one. Consider the example:

Passage of the law means morality is corrupted. (p, q)

If we analyze the proposition, it is very clear that it is a conditional proposition because
it suggests a “cause and effect” relation. Thus, the proposition can be stated as follows:

If the law is passed, then morality will be corrupted.

If we let p stand for “The law is passed” and q for “Morality will be corrupted,” then the
proposition is symbolized as follows:

p⊃q

It is also important to note that sometimes the antecedent is stated after the
consequent. If this happens, then we have to symbolize the proposition accordingly.

Let’s take the example below.

Morality would be corrupted should the abortion law is passed. (p, q)