1. In the first chapter of our textbook, Section 1.1 "The origins of Mathematical Logic", the author states

that Logic must be formalized because reasoning expressed in informal natural language can be flawed.

As a proof, he cites an example of a flawed syllogism given in 1978 by Smullyan:

Premise: Some cars rattle.

Premise: My car is some car.

Conclusion: My car rattles.

What is wrong with that syllogism?

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2. The Lecture Notes states "Eventually it (Mathematical Logic) became also part of the foundations of

Computer Science, serving both a theoretical and a practical purpose." Please explain:

(a) The theoretical importance of Mathematical Logic

(b) The practical importance of Mathematical Logic

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3. Let P, Q and R be sets, P R, Q R. Are the following expressions true or false? Explain why.

(a) P = (P Q) P

(b) P Q = (P Q) Q

(c) (P Q)C = PC Q

C

(d) P R = P

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4. Let P, Q and R be the sets

P = { n | n , 2 n 10 }

Q = { n | n , 5 < n 20 }

R = { n | n , 1 n < 10 }

Find:

(a) P (Q R)

(b) QC (P R)

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5. Let S = {1, 2, 3, 4}. List the members of the powerset of S.

(The powerset of a set S, denoted 2S

, is defined as the set of all subsets of S, including and S itself)