Question

Which of the following x does not satisfy r(x) in the given predicate using the ! symbol?

1) x = 1
2) x = 2
3) x = 3
4) x = 4

Answer 1

None of the given x values (1, 2, 3, 4) fail to satisfy the predicate r(x), as they are all different from 0. The predicate is only undefined and fails at the origin, where x = 0.

Step-by-step explanation:

The provided information suggests the existence of a function r(x) that is undefined at the origin, where x = 0, y = 0, and thus r = 0. The notation ! likely stands for 'not,' which indicates we are looking for values of x that do not satisfy the function r(x).

Since all given options (x = 1, 2, 3, 4) are nonzero, they do not correspond to the point where the relations fail, which is exclusively the origin (x = y = r = 0). Therefore, none of the listed x values (1, 2, 3, or 4) fail to satisfy the predicate r(x) because they are all different from 0. The predicate r(x) would only be unsatisfied if x were equal to 0.