CS 281 Test I

June 2, 1998

1. Express the assertions given below as a proposition of a predicate logic using the following predicates. The universe is the set of objects.[25]

B(x): x is a bee.
F(x): x is a flower.
Y(x): x is yellow.
L(x,y ) : x loves y.

(a) There are no yellow flowers.
(b) Every bee is yellow.
(c) Not every bee loves flowers.
(d) All bees love some flowers.
(e) Some bees love only flowers.

2. Fill in the blanks with the shortest string of characters so that the resultant proposition is valid. [24]

(a) (Other than Q)
(b)
(c)
(d) .
(e) ]

3(a) Negate each of the propositions given below using the following symbols. Give a form other than simply putting in front. [8]

p: It is below freezing.
q: It is snowing.

(1) It is below freezing and snowing.
(2) It is below freezing but not snowing.
(3) If it is below freezing, it is also snowing.
(4) It is snowing only if it is below freezing.

3(b) Find the converse and the contrapositive of the propositions (3) and (4) of 3 (a). Also do the same for the negation of (1) and (2). State then in English.[24]

4(a) Express the argument given below using a symbol for each proposition. [5]
(b) Using the symbols of (a) for the propositions, explain how the reasoning proceeds i.e. identify each application of inference rule in the argument. Is the reasoning correct ? Give your reasons. [14]

Argument:
It is not the case that IBN or Yerox will take over the copier market. RCB returns to the computer market only if IBN will take over the copier market. Hence, RCB will not return to the computer market.

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