I Don't understand the use of ^ in Java

Question

I have this code.

int a = 10;
int b = 20;
int c = 6;

System.out.println(a > b ^ a > c);

The output is true, I don't understand what ^ does, why is the output true? what is the main function of ^ when is inside of one conditional?

Answer 1

^ is bitwise exclusive OR operator .
It's truth table is:
P Q R
0 0 0
0 1 1
1 0 1
1 1 0

So it gives result 1(true) if and only if one of the two propositions is 1(true)

Also priority of operator ^ is less than both < and > so first a>b and a>c get evaluated.
a>b is false (10<20 is false)
a>c is true (10>6 is true)

now false ^ true corresponds to column
0 1 in the truth table. so answer is 1(true)

Answer 2

^ is a bitwise XOR its operator precedence is lower than that of < or > so it will happen after those complete.
a > b = false
a > c = true
false ^ true = true

false = 0
true = 1

XOR Table
^ 0 1
0 0 1
1 1 0

false ^ false = false
true ^ true = false
true ^ false = true
false ^ true = true

Basically with an XOR if the comparing bits are the same the resulting bit is 0 otherwise 1.