 The implication, if then, is less similar to its corresponding expression in natural language than any other logical connective. In propositional logic, it is usually called the material implication, and it is only false if its antecedent P, the if clause, is true, and its consequent Q, the then clause, is false. The material implication is symbolized by a forward arrow or by the algebra symbol that is also used for sets. Let us look at an example and construct the truth table. If Brutus kills Caesar, then Caesar will be dead. This implication is certainly true if both antecedent P and consequent Q are true. But it is also true if the antecedent P is false, that is, Brutus did not kill Caesar since now the consequent Q cannot be invalidated. Caesar could still be dead. However, if Brutus did kill Caesar but Caesar is not dead, that is, P is true and Q is false, the implication is false too. And if both P and Q are false, as in, if Brutus did not kill Caesar, then Caesar will not be dead, the implication is true too. So the crucial case is the third condition. If P then Q is false, if and only if the antecedent P is true and the consequent Q is false. This is the material sense of the implication where there is no necessary connection between antecedent and consequent. Thus, in summary, unlike as the natural language construction may, the conditional statement if P then Q does not specify a causal relationship between the antecedent and the consequent. Rather, it is to be understood to mean if P is true, then Q is also true.