Question 1207017
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I'll use an arrow symbol in place of the horseshoe symbol.
Also, I'll use an ampersand in place of a dot.


Here is one way to do the derivation.
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr><tr><td>1</td><td>S --> (L & M)</td><td></td><td></td></tr><tr><td>2</td><td>M --> (L --> R)</td><td></td><td></td></tr><tr><td>:.</td><td>S --> R</td><td></td><td></td></tr><tr><td>3</td><td>(M & L) --> R</td><td>2</td><td>Exportation</td></tr><tr><td>4</td><td>(L & M) --> R</td><td>3</td><td>Commutation</td></tr><tr><td>5</td><td>S --> R</td><td>1, 4</td><td>Hypothetical Syllogism</td></tr></table>


The Rules of Inference and Rules of Replacement are shown <a href="https://www.algebra.com/algebra/homework/Conjunction/logic-rules-of-inference-and-replacement.lesson">here</a>
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