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(b) Now consider an chessboard for some fixed . For , how manyke squares are contained in this chessboard?

其他申論題

2.Verify that, for primitive statements and.

(a) Write a quantified statement to express the proper subset relation .

(b) Negate the result in part (a) to determine when .

4. (a) Consider an chessboard. It contains eighty-one squares and one square. How many squares?

5. Let be a set of five positive integers the maximum of which is at most 9. Prove that the sums of the elements in all the nonempty subsets of S cannot all be distinct.

6. Given a nonempty language , prove that if, then.

7.(a) Find the coefficient of.

(b) Find the coefficient offor .

8.Let with . Prove that if and , then .

(a) there must be seven men and seven women?

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