Why A==(A or B) is True, while B==(A or B) is False?

Question

I have very simple program to write, which check if input is A or B. I know I could go for:

if input() == A or input == B:
print("Ok")

But why you can't make something like this?

if input() == (A or B):
print("Ok")

In this scenario
A == (A or B) is True
B == (B or A) is True
But
A == (B or A) is False
B == (A or B) is False

Theoretically it's true when
True==(False or True) changing it to numbers (1=0+1)

Is it because strings don't have logic value of 1 prior to checking it with == ?
Why would then A==(A or B) work?
I'm bit confused.

Answer 1

All you need to know how or operator works.
or returns the first Truthy value if there are any, else return the last value in the expression.

print( x or y)
It means if x is a Truthy value x is returned, y vice versa.
Now, you can think about that cases.

Answer 2

You need to store the value of input & then compare it separately.

if input() == ('A' or 'B') mean if input() == 'A' or 'B' so, here we didn't actually defined any clear logic for the second case.

Answer 3

Piotr Ś
We have to check the equality of B just like we did with the A.

x = input()

if x == 'A' or x == 'B':
print('ok')

Answer 4

Ah ok, so statement after "or" is "whatever, we already got our True, don't bother with mess after "or" "?