CS 281 Test I
July 11, 1995
1. For the following proposition find an equivalent proposition which uses only and , and simplify the resultant proposition as much as possible:


2. Fill in the blanks with the shortest string of characters so that the resultant proposition is valid.

(a)
(b)
(c)
(Other than ).
(d)

3. Simplify the following proposition:


4. Express the assertions given below as a proposition of a predicate logic using the following predicates. The universe is the set of integers.

A(x,y,z): x + y = z,
E(x): x is even,
G(x,y): x > y,

(a) Every integer is greater than 1, if it is even and positive.
(b) There is no odd integer which is greater than any integer.
(c) There is an even integer which is greater than any nonnegative odd integer.
(d) If an even integer is added to an odd integer, then the result is odd.
(e) For an integer to be odd, it is necessary that adding an odd integer to it produces an even integer.
(f) An integer is greater than 1 only if it is positive.

5. Find the converse and the contrapositive of question 4(f) above. State them in English.

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