Careless Mistake

Thursday, January 22, 2009 at 2:15 PM | Filed under

I'm taking Math 300, where we deal with all sorts of math reasoning, proofs, and logic. I got back one of my homework problems. The question was this:
A certain island is inhabited by two tribes of people. The members of one tribe always make true statements, and the members of the other tribe always make false ones. (And they are all skillful logicians.) The natives all know who is a truth-teller and who is a liar, but a visitor cannot tell the truth-tellers from the liars just by looking at them. . . . Suppose you meet three natives — A, B, and C — and the first two make the following statements:

A: B is a liar.
B: If A is a liar, then so is C.

Using only this information, figure out whether A, B, and C are truth-tellers or liars, and explain your reasoning.
And I made a rather careless mistake, right at the end:

Ack! I lost one point out of ten for this...


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