Elaborate Geometry
As you can see, there is a big difference in deductive and inductive reasoning. However, you can apply them both in math, and from there, to the real world. A prime example is a store. If milk is $1 per gallon, you can conclude, by deductive reasoning, that 2 milks would cost $2. The p → q statements for this example would be if you buy 1 milk, then it costs $1. The conjecture or statement you believe to be true using inductive reasons, for this statement is 2 milks cost $2.
In the statement "If you buy 1 milk, then it costs $1", the phrase, "If you buys one milk" is called the hypothesis. The statement "then it costs $1" is called the conclusion. In any statement that can be written as p → q, the p is the hypothesis and the q is the conclusion. Any statement that can be written in this way is called a conditional statement.
The law of detachment states this as well.
(PICTURE: Law of detachment)
A further elaboration of this idea is the law of syllogism.
(PICTURE: Law of Syllogism)
An everyday example of Inductive reasoning is the scientific method. The scientific method, when used properly, tests an investigative question by going through the process of scientific steps. Another person or laboratory, when duplicating this experiment, should give the exact same result. If the experiment is followed exactly and a different result is achieved, the first experiment cannot become a law or given.
An example of Deductive reasoning is this "To run for ASB President, you must be a senior in high school. Andy is not a senior." The conclusion you can draw is that Andy cannot run for ASB President.
As you can see, Inductive and Deductive reasons are used every day.
Try this question!
A) Triangle XYZ is isosceles. All isosceles triangles have two equal angles. Describe triangle XYZ. Be sure to mention about the sides of the triangle.
After writing your answer, move on to EVALUATE!