1.91 The table below shows the value of a predicate M(x, y) for every possible combination of values of the variables x and y. The domain for x and y is {1, 2, 3}. The row number indicates the value for x and the column number indicates the value for y. For example M(1, 2) = F because the value in row 1, column 2, is F. M 1 2 3 1 T F T 2 T F T 3 T T F

Indicate whether each of the logical expressions is a proposition. If so, indicate whether the proposition is true or false.

(f) M(x, 2)

7.5 In the following question, the domain of discourse is the set of employees of a company. Define the following predicates:

A(x): x is on the board of directors E(x): x earns more than $100,000 W(x): x works more than 60 hours per week

Translate the following logical expressions into English:

(d) x (A(x) E(x))

(e) x (E(x) (A(x) W(x)))

(f) x (A(x) E(x) W(x))