优化条件

Question

I want to simplify this condition where a and b are booleans

!((a && b) || (!a && !b))

I have tried using the truth table generator, but I am not able to figure out the simplified version.

Answer 1

This can be simplified as a XOR (exclusive or). It's equivalent to (a && !b) || (!a && b) (a && !b) || (!a && b) .

In Java, it can be achieved as a ^ b

Answer 2

You can simplify this in : a!=b ,

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Because, by equivalence :

!((a && b) || (!a && !b)) // not(both true or both false)
!(a==b)                   // not(both equals)
a!=b                      // different

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And here is the table, which confirms that you a different of b :

 a\b  | true  | false
true  | false | true
false | true  | false

Answer 3

You could simplify to either if (!(a==b)) or if (a!=b) .

Your condition simplifies to "if a and b are both true (ie, of equal state) or both false, then condition resolves to false". Or "if a is a different state to b, condition resolves to true".