The ⊻ (exclusive or) symbol is used in logic and mathematics to denote a logical operation that outputs true only when the number of true inputs is odd. It could be used in an expression like this:
In plain language, this means that the statement is true if exactly one of or is true, but not both.
The logical-and symbol is used in math as a logical operator.
The logical or symbol is used in logic and mathematics to denote the logical disjunction operation. It's true if at least one of the operands is true.
The negation symbol is used in math to represent the logical negation operator.