1.91 The table below shows the value of a predicate M(x, y) for every possible c
ID: 3885616 • Letter: 1
Question
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))
Explanation / Answer
1.91
proposition is something that can be considered either TRUE or FALSE.
M(x,2) is not a proposition. The domain of x is {1,2,3}. So, M(1,2)=F, M(2,2)=F, M(3,2)=T. So, it has different value for different x.
7.5
Check the logic symbols for "there exists", "for all", "and", "or" . According to the symbols these are the expressions in english.
d) there are employees who are not on board of directors and earns more than $100,000
e) All employees who earns more than $100,000 either on board of directors or works more than 60 hours per week.
f) there are employees who are not on board of directors and doesnot earn more than $100,000 and also works more than 60 hours per week.
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