The tables below show the values of predicates P(x, y), Q(x, y), and S(x, y) for

Question

The tables below show the values of predicates P(x, y), Q(x, y), and S(x, y) for every possible combination of values of the variables x and y. The row number indicates the value for x and the column number indicates the value for y. The domain for x and y is {1, 2, 3}.

Indicate whether each of the quantified statements is true or false.

(a)

x y P(x, y)

(b)

x y Q(x, y)

(c)

x y P(y, x)

(d)

x y S(x, y)

(e)

x y Q(x, y)

(f)

x y P(x, y)

(g)

x y P(x, y)

(h)

x y Q(x, y)

(i)

x y ¬S(x, y)

P 1 2 3 1 T F T 2 T F T 3 T T F Q 1 2 3 1 F F F 2 T T T 3 T F F S 1 2 3 1 F F F 2 F F F 3 F F F

Explanation / Answer

(a)

x y P(x, y)
= There exists a row in P where all the values are True
False

(b)

x y Q(x, y)
= There exists a row in Q where all the values are True (2nd row)
True

(c)

x y P(y, x)
= Every row has some value that is True in P
True

(d)

x y S(x, y)
= Some value in the whole S is True
False

Note: 4 sub parts at a time please -- Policy of Chegg

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