The converse of the contrapositive of the conditional p→∼q is :
converse of a→b is b→a
contrapositive of a→b is ~b→~a
so,
the contrapositive of p→~q is ~(~q)→~p, or q→~p
the converse of q→~p is ~p→q
To find the converse of the contrapositive of the conditional p → ¬q, let's first determine the contrapositive of p → ¬q.
The contrapositive of p → ¬q is ¬(¬q) → ¬p.
Simplifying ¬(¬q) to q, we get q → ¬p.
Now, to find the converse, we need to switch the positions of q and ¬p in the statement q → ¬p.
Therefore, the converse of the contrapositive of the conditional p → ¬q is ¬p → q.
To determine the converse of the contrapositive of the conditional p→∼q, we first need to understand what the contrapositive and converse of a conditional statement are.
A conditional statement is of the form "if p, then q." In this case, the conditional is p→∼q.
The contrapositive of a conditional statement flips its antecedent (p) and its consequent (q), and negates both. So the contrapositive of p→∼q is ∼∼q→∼p, which simplifies to q→∼p.
Now, the converse of a conditional statement also flips its antecedent and consequent, but it does not negate them. Therefore, the converse of p→∼q is q→p.
So, the converse of the contrapositive of p→∼q is q→p.