In Discrete Mathematics, I need some help with creating a problem like this one
ID: 3110797 • Letter: I
Question
In Discrete Mathematics, I need some help with creating a problem like this one below: 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.
Indicate whether each of the logical expressions is a proposition. If so, indicate whether the proposition is true or false.
(a) M(1, 1)
(b) y M(x, y)
(c) x M(x, 3)
(d) x y M(x, y)
(e) x y M(x, y)
(f) M(x, 2) (g) y x M(x, y)
I'm trying to understand this,
M 1 2 3 1 T F T 2 T F T 3 T T FExplanation / Answer
a)M(1,1)=T ,because the value of row is 1,the value of column is 1,is T.
b)For all y column,M has different values
c)some x,M has different values in 3rd column i.e T,T,F.
d)some x ,y ,M has different values.
e)In some x,all y ,M has different values
f)M(x,2)=F,F,T
because xth row and 2nd column has value F,F,T
g)In some y,all x,Mhas different values