Answer:
Converse, Inverse, and Contrapositive
With aspects of the implication in our rear view mirror, we now want to form new compound statements from that original implication. These new statements are called the converse, inverse, and contrapositive statements.
Converse
For two statements P and Q, the converse of the implication "P implies Q" is the statement
Q implies P.
The converse of "P implies Q" is more commonly written as follows
If Q, then P.
with the truth values of the converse of "P implies Q" given in the last column of the following truth table.
P Q P implies Q Q implies P
T T T
T
T F F T
F T T F
F F T T
After looking at the last two columns of the truth table, we immediately notice that the implication and the converse take on different truth values when there is one simple statement (either P or Q) being true and the other statement being false. This leads to some confusion at times, however it is important to note the differences between these two compound statements, which we shall explore below.
Step-by-step explanation:
