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 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)