what is the difference between xor and or in Haskell

Question

So, if xor returns True if and only if exactly one of its operands is True such that:

xor :: Bool -> Bool -> Bool
xor True True = False
xor True False = True
xor False True = True
xor False False = False

My question is: would or be similar but return True if one or both of its operands is True ?

Answer 1

you can write xor simply as

 xor a b = a /= b

also or can be simplified

 or True _ = True
 or False b = b

For fun, you can define all logical functions in terms of nand.

 nand :: Bool -> Bool -> Bool
 nand True True = False
 nand _ _ = True

not is easy

 not a = nand a a

and requires two gates

 and a b = not (nand a b)

or , requires three

 or a b = nand (not a) (not b)  

and, xor requires four

 xor a b = let z = nand a b in nand (nand z a) (nand z b)