16.2. If-Then Statements http://www.ck12.org
In this case setPis a subset of setQsince it is entirely included within setQ. Mathematically we write the statement
“Pis a subset ofQ” as:
P⊆Q
This can be translated to an if-then statement, and simplified using symbols:
If it is an element in P, then it is an element in Q.
If P, then Q.
P→Q
If-then statements are examples ofconditional statements. Sometimes conditional statements are written without
an “if” or a “then”, but can be rewritten. The “if” part of the statement (represented byPabove) is called the
hypothesis, antecedentorprotasis. The “then” part of the statement (represented byQabove) is called the
conclusion, consequentorapodosis.
In order to precisely define the truth value of a conditional statement, we need to consider the four different
combinations of the truth value forPandQin relation to the diagram
1.If P is true, then Q is true.This statement is true because if an object is inside circleP, then it is definitely