No, it is not valid because there is no operator between P and q.
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A+
Any fraction p/q where p is an integer and q is a non-zero integer is rational.
Call the numbers p and q. From the problem statement, p - q = 16 and p + q = 58. From the first of these, p = q + 16. Substitute this in the second to result in q + 16 + q = 58, or 2q = 58 - 16, or q = 21, and p = 37. Alternatively 58 - 16 = 42. 42/2 = 21 and 21 + 16 = 37. Same result, different method.
q + p
If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)