By Edward A. Bender

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**Extra info for A Short Course in Discrete Mathematics**

**Sample text**

Let’s do some examples. ” This is false if something is a fish and does not require water. In general “A requires B” is false when A is true and B is false. Thus, we have A ⇒ B. ” This is false if I receive credit even though I am not enrolled. In other words “A is necessary for B” is false when B is true and A is false. Thus we can write it as B ⇒ A. ” This is false when I don’t flunk and I don’t study. Thus, it is false when A and B are both false. Since we need (True)⇒(False), we need to negate something.

In octal, the twelve-bit two’s complement of the hexadecimal number 2AF16 is (a) 65228 (b) 62518 (c) 52618 (d) 65128 (e) 65218 Answers: 1 (c), 2 (a), 3 (d), 4 (e), 5 (b), 6 (a), 7 (d), 8 (a), 9 (c), 10 (b), 11 (d), 12 (e). BF-25 Unit Lo Logic Logic is the tool for reasoning about the truth and falsity of statements. There are two main directions in which logic develops. • The first is the depth to which we explore the structure of statements. The study of the basic level of structure is called propositional logic.

It is easy to factor F5 with modern computers, but it was hard when people computed by hand. , Fermat numbers that are prime)? ” No one knows which assertion is correct. It is known that F6 through F20 are, like F5 , composite. 2 This is not the same as the predicate R in Example 9. Explain why. Express S(x) in terms of R. Lo-16 Section 2: Predicate Logic High school math students who take geometry often suffer through “straight edge and compass” constructions of various geometric figures. The ancient Greeks figured out that any regular polygon with 3 · 2k sides, k ∈ N, or with 5 · 2k sides, k ∈ N could be constructed with straight edge and compass.

### A Short Course in Discrete Mathematics by Edward A. Bender

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