Show that the following propositions are logically equivalent using logical transformations (not using truth tables) p→q≡~q→~p

To show that the propositions p→q and ~q→~p are logically equivalent, we can apply logical transformations.

Starting with p→q, we can use the definition of implication to rewrite it as ~p∨q.

Next, we can use De Morgan's law to further transform it as ~(p∧~q).

Now let's look at ~q→~p. Using the definition of implication, we can rewrite it as ~(~q)∨~p.

Applying double negation, ~(~q) becomes q, so ~q→~p can be written as q∨~p.

By comparing ~(p∧~q) with q∨~p, we can see that they are the negations of each other. Therefore, they are logically equivalent.

Answer: p→q≡~q→~p