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How to show, using logic table: $(P\rightarrow Q)\land(Q\rightarrow R)$ is logically equivalent to $(P\rightarrow R)$?

I had 8 rows, and found the truth values for $(P\rightarrow Q)$, $(Q\rightarrow R)$, $(P\rightarrow Q)\land(Q\rightarrow R)$, which lead to the truth values for $(P\rightarrow R)$. However, these values were not equivalent with $(P\rightarrow R)$ (their truth values were different even with the same truth values of $P, Q$, and $R$ )

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    $\begingroup$ They are not logically equivalent. $\endgroup$ Commented Sep 10, 2015 at 4:34

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They are not logically equivalent. There is a logical implication, but it only goes one way.

$$\underbrace{(P\to Q ) \wedge (Q\to R)}_{\text{antecedant}} \;\implies\; \underbrace{(P\to R)}_{\text{consequent}}$$

Your truth table should show that the antecedent is true whenever the consequent is; but not necessarily the other way about.

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