Which of the following are logically equivalent?

A. $\neg p\to(q\to r)$ and $q\to(p\lor r)$

B. $(p\to q)\to r$ and $p\to(q\to r)$

C. $(p\to q)\to(r\to s)$ and $(p\to r)\to(q\to s)$

Choose the correct answer from the options given below:

Check A:

$\neg p\to(q\to r)\equiv p\lor(\neg q\lor r)$

$=p\lor\neg q\lor r$

Also,

$q\to(p\lor r)\equiv\neg q\lor p\lor r$

Both are same, so A is true.

Check B:

$(p\to q)\to r\equiv(p\land\neg q)\lor r$

$p\to(q\to r)\equiv\neg p\lor\neg q\lor r$

Both are not always same, so B is false.

Check C:

Both expressions are not always logically equivalent.

So, C is false.

Therefore, only A is correct.