The Transitive Property of Implication in Logic and Mathematics | Understanding the Chain of Events from p → q and q → r to p → r

if p → q and q → r , then p → r

In logic and mathematics, the statement “p → q” represents an implication or conditional statement, which can be read as “if p, then q” or “p implies q

In logic and mathematics, the statement “p → q” represents an implication or conditional statement, which can be read as “if p, then q” or “p implies q.” This statement asserts that if p is true, then q must also be true.

Similarly, the statement “q → r” represents another implication, suggesting that if q is true, then r must also be true.

Given these two implications, we can apply a logical rule known as the transitive property of implication to deduce that “p → r.” The transitive property states that if a implies b and b implies c, then a implies c. In this case, we have “p → q” and “q → r,” so we can conclude that “p → r” is true.

To understand this intuitively, imagine a chain of events. If p leads to q, and q leads to r, then it makes logical sense that p must also lead to r, even if there is an intermediate step with q.

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