This is about negations of if then statements and why they can't be if then statements.
explain why the negation of an if then statement can not be an if then statement
Perhaps a Truth Table might shed some light on this. Below is a TT for "if p, then q."
p. q. if p, then q.
T. T. T.
T. F. F. [note this case. "if T, then F" = F.]
F. T. T.
F. F. T.
Notice that an implication "if p, then q" is only F when then premise, p, is T and the conclusion, q, is F.
This is also the only case the negation of an implication is T.
So considering this, we see that a negation of an "if-then", being true in only one case, cannot also be an "if-then", which is T in three cases.
Incidently, the negation of "if p, then q" is "p and (not q)."
Hope that helps.
The negation of an if/then statement cannot be an if/then statement because the negation is a selection, or choice, whereas an if/then statement is conditional. The if/then statement merely states a causal relation between two possibilities but it does not guarantee the outcome or actuality of these possibilities. For example, "if A, then B" means that if it is true that A is, then B is too; however, it does not establish that A is or B is. The negation of this if/then statement, "A, but not B," is a negation in the sense that it is an outcome which establishes that B does not necessarily follow from A, or, in other words, it proves that the relation stated in the if/then statement is false.