Simple Logic

Arguments consist of premises (statements) followed by a conclusion. To be valid, the premises must support the conclusion.
The structure of the argument starts with the premises:

• All A are B. All C are A.

The premises are followed by the conclusion:

• All C are A, therefore all C are B.

The first example:

• Let A = rainy days and B = cloudy days. Let C = Tuesday.
  

Here are the premises to the above example:

• All rainy days (A) are cloudy days (B). On (C) Tuesday it rains (A).

The conclusion:

• Tuesday (C) there is rain (A), therefore Tuesday (C) there are clouds (B). All A are B. All C are A. Therefore all C are B.

We can have some fun with this:

Switch A and B around in the conclusion and see how this becomes invalid:

• Tuesday (C) there are clouds (B), therefore Tuesday (C) there is rain (A).

The second example:

• All Geeks (A) love computers (B). Bill (C) is a Geek (A).

The conclusion:

Bill (C) is a Geek (A), therefore Bill (C) loves computers (B).

Make the above argument invalid:

The examples above are termed syllogisms, forms of deductive reasoning. We use syllogistic reasoning in its valid and invalid forms often. There are four valid forms we use.

For example: All A are B. C is A. Therefore C is B. (used above)
No A are B. C is A. Therefore C is not B.
Some A are B. C is A. Therefore some C are B.
Some A are not B. C is A. Therefore some C are not B. (Whew!)

Which is this? Is it valid or invalid?

When the Xerox machine is out of paper, jammed or lacking ink, it spits out the original and stops. Yesterday the Xerox machine stopped, therefore it must be out of paper.

Follow this link to an interesting site on deductive logic.