Discrete Math: Indicate whether each of the logical expressions is a proposition

Question

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

(c)x M(x, 3)

(d)x y M(x, y)

(e)x y M(x, y)

(g)y x M(x, y)

EXERCISE 1.9.1: Which logical expressions with nested quantifiers are propositions? 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, isF M 12 3

Explanation / Answer

1.true,it is a propostion as x is defined.

there should be atleast one (x,3) here x is in the rows should be true

which we have in row 1 and row 2.

2.true. it is a proposition as x and y are defined.

m(x,y) is true for at least one x and one y.

3.false . it is propsition as x and y are defined.

m(x,y) there does not exist a row in which every element is true.

4.true. it is a proposition as x and y are defined.

m(x,y) ther exists a y first column where for y every x is true.

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