Question

The trivial negation of a proposition is: “It is not the case that [proposition]." Write two negations of the following, one trivial and one not trivial.

(a) It is snowing. (b) At least 3 inches of snow fell yesterday. (c) 1 + 2 = 3.

Answer 1

a) It is snowing

trivial) It is not the case that it is snowing

not trivial) There exists at least one which is not snowing

b) At least 3 inches of snow fell yesterday

trivial) It is not the case that at least 3 inches of snow fell yesterday

not trivial) There exists at least one of 3 inches of snow which fell yesterday

b) 1 + 2 = 3

trivial) It is not the case that 1 + 2 = 3

not trivial) There exists at least one expression when 1 + 2 $\neq$ 3