p ⊕ q
The symbol ⊕ denotes the exclusive OR (XOR) operation in mathematics
The symbol ⊕ denotes the exclusive OR (XOR) operation in mathematics. It is a binary operator that takes two Boolean values (usually denoted as p and q) and returns true if exactly one of the operands is true, and false otherwise.
To understand how the XOR operation works, we can consider the following truth table:
p | q | p ⊕ q
—————-
T | T | F
T | F | T
F | T | T
F | F | F
From the truth table, we can see that if both p and q are true, or both are false, then p ⊕ q evaluates to false. However, if exactly one of p or q is true, then p ⊕ q evaluates to true.
The XOR operation is commonly used in many areas of mathematics, computer science, and information theory. It has applications in cryptography, error detection and correction, and logic circuits.
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