When we previously discussed inductive reasoning we based our
reasoning on examples and on data from earlier events. If we
instead use facts, rules and definitions then it's called deductive
We will explain this by using an example.
If you get good grades then you will get into a good
The part after the "if": you get good grades - is called a
hypotheses and the part after the "then" - you will get into a good
college - is called a conclusion.
Hypotheses followed by a conclusion is called an If-then
statement or a conditional statement.
This is noted as
This is read - if p then q.
A conditional statement is false if hypothesis is true and the
conclusion is false. The example above would be false if it said
"if you get good grades then you will not get into a good
If we re-arrange a conditional statement or change parts of it
then we have what is called a related conditional.
Our conditional statement is: if a population consists of 50%
men then 50% of the population must be women.
If we exchange the position of the hypothesis and the conclusion
we get a converse statement: if a population consists of
50% women then 50% of the population must be men.
If both statements are true or if both statements are false then
the converse is true. A conditional and its converse do not mean
the same thing
If we negate both the hypothesis and the conclusion we get a
inverse statement: if a population do not consist of 50%
men then the population do not consist of 50% women.
The inverse is not true juest because the conditional is true.
The inverse always has the same truth value as the converse.
We could also negate a converse statement, this is called a
contrapositive statement: if a population do not
consist of 50% women then the population do not consist of 50%
The contrapositive does always have the same truth value as the
conditional. If the conditional is true then the contrapositive is
A pattern of reaoning is a true assumption if it always lead to
a true conclusion. The most common patterns of reasoning are
detachment and syllogism.
If we turn of the water in the shower, then the water will stop
If we call the first part p and the second part q then we know
that p results in q. This means that if p is true then q will also
be true. This is called the law of detachment and is noted:
The law of syllogism tells us that if p → q and q → r then p → r
is also true.
This is noted:
If the following statements are true:
If we turn of the water (p), then the water will stop pouring
(q). If the water stops pouring (q) then we don't get wet any more
Then the law of syllogism tells us that if we turn of the water
(p) then we don't get wet (r) must be true.
Video lesson: Write a converse, inverse and
contrapositive to the conditional
"If you eat a whole pint of ice cream, then you won't be