whose external nodes are associated with variables or constantsand whose internal nodes are associated with one of the operators +-xand (see figure each node in such tree has value associated with it if node is externalthen its value is that of its variable or constant if node is internalthen its value is defined by applying its operation to the values of its children an arithmetic expression tree is proper binary treesince each operator +-xand takes exactly two operands of courseif we were to allow for unary operatorslike negation (-)as in "- ,then we could have an improper binary tree figure binary tree representing an arithmetic expression this tree represents the expression (((( )/(( - + )(( ( - ) )the value associated with the internal node labeled "/is