I hope this is a simple question but I just wanted to get confirmation and also the intuition behind it.
I know the put call symmetry and I often see it expressed as: Call(S, K) = Put(K, S) = K/S Put(S, S^2/K) where S is the spot and K is the strike.
I was wondering if it is the same from the perspective of Puts, i.e.: Put(S, K) = Call(K, S) = K/S Call(S, S^2/K)
Thank you in advance for any help