If we call the first part p and the second part q then we know that p results in q. If we turn of the water in the shower, then the water will stop pouring. The most common patterns of reasoning are detachment and syllogism. If the conditional is true then the contrapositive is true.Ī pattern of reaoning is a true assumption if it always lead to a true conclusion. The contrapositive does always have the same truth value as the conditional. 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% men. The inverse always has the same truth value as the converse. The inverse is not true juest because the conditional is true. 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. A conditional and its converse do not mean the same thing If both statements are true or if both statements are false then the converse is true. 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. Our conditional statement is: if a population consists of 50% men then 50% of the population must be women. If we re-arrange a conditional statement or change parts of it then we have what is called a related conditional. The example above would be false if it said "if you get good grades then you will not get into a good college". Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.Ī conditional statement is false if hypothesis is true and the conclusion is false. 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.
If you get good grades then you will get into a good college.
We will explain this by using an example. If we instead use facts, rules and definitions then it's called deductive reasoning. When we previously discussed inductive reasoning we based our reasoning on examples and on data from earlier events.
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