A material conditional P --> Q is true unless P is true and Q is false.
The proposition P --> Q can be true even if P is false (Q must be false). The proposition P --> Q can be false even if P is true (Q may be true or false).
You may assume the Peano Axioms to be true or to be false, there is no right or wrong.
A material conditional P --> Q is true unless P is true and Q is false.
The proposition P --> Q can be true even if P is false (Q must be false).
The proposition P --> Q can be false even if P is true (Q may be true or false).
You may assume the Peano Axioms to be true or to be false, there is no right or wrong.