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The second rule listed here is not necessarily true. While the truth of R is dependent on the truth of Q, truth of Q is not dependent on the truth of R. Try this: "If Mike Huckabee is elected President, his wife will be First Lady. Mrs. Huckabee is not first lady, therefore Mike was not elected President." However, there are (logically, anyways) ways in which Mike could be President without Mrs. Huckabee being First Lady - they could get divorced, the position of First Lady could be abolished, what have you. Is therea logician arouns who could clear this up? Walt 23:42, 23 November 2007 (EST)

It seems that someone raised the point I wish to raise a long time ago. The second rule is not deduction, it is induction, since produces a conclusion that goes beyond the available evidence.

If Q is true, then R is true. If we say "Q is true" then we can deduce that R is also true.

But, if we say "R is true" then it does not logically follow that Q is true, nor is is the case if in both instances we swap true with not true. Indeed, if R is true then it is possible that Q is also true, but we cannot conclude that it definitely is. As such, I have deleted the second rule. DWiggins 21:36, 29 October 2009 (EDT)

Incorrect example

If A is true then B is true.

If A is true then given this premise there is only one conclusion that we can be totally certain of, that B is also true.

We cannot say for sure that if B is not true then A will no be true. This is not supported by the premise. The premise states only the relationship of B dependent upon A, not vice versa. Of course we could guess, given that true or false are the only options here, but there is no premise to support the conclusion that if B is not true then A is not true. It is not the easiest concept to explain through a means such as this, but I'm afraid I am correct and I will remove the example again if it is added, for it is not an example of deduction. DWiggins 22:20, 30 October 2009 (EDT)

No, you are wrong. Unless one is using some kind of bizarre non-binary "logic", or "fuzzy logic" (a computer science term that is not the same as mathematical logic), or some extreme interpretation of intuitionistic logic, the example I put back is perfectly valid. It's called the "contrapositive", and its logical correctness has been used since the time of Euclid. PatrickD 23:12, 30 October 2009 (EDT)