Let a be a random assignment. Let's extend propositional logic L with a new operator *, which accepts two arguments and has the following properties: [T* 1]" + [1 *T]and [T*T]" # [1*1]. In other words, * evaluates differently if both its arguments evaluate to the same value and if both arguments evaluate to a different value. The set of propositional formulas, which uses only the operators from the set {T, 1, *}, is called L*. For each operator, that has the properties of *, show, that there's always a propositional formula WEL, for which no equivalent formula &' E * exists. Hint: Use structural induction for your proof. There are four different operators with the given pro- perties. Let a be a random assignment. Let's extend propositional logic L with a new operator *, which accepts two arguments and has the following properties: [T* 1]" + [1 *T]and [T*T]" # [1*1]. In other words, * evaluates differently if both its arguments evaluate to the same value and if both arguments evaluate to a different value. The set of propositional formulas, which uses only the operators from the set {T, 1, *}, is called L*. For each operator, that has the properties of *, show, that there's always a propositional formula WEL, for which no equivalent formula &' E * exists. Hint: Use structural induction for your proof. There are four different operators with the given pro- perties