While modus ponens is one of the most commonly used concepts in logic it must not be mistaken for a logical law; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the "rule of definition" and the "rule of substitution".
In simple words, mathematical logical and the subject of statistics include logical derivations and inferences. Each incident or occurrence or phenomenon is supposed to depend on the occurrence (or non occurrence) of another dependent incident or occurrence or phenomenon. Hence, if we have confirmed that occurrence of incident ‘P’ implies that incidence of, say ‘Q’ is bound to occur. Then if P has already occurred, it can be concluded that ‘Q’ has occurred too. Many a time, the reverse is assumed too. I.e. If P implies Q, and if Q has occurred, it is implied that P has also occurred. But this gives rise to a fallacy that the reverse logic may or may not be true.
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