Question 1207022
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I'll use an arrow symbol in place of the horseshoe symbol.
<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>T --> R</td><td></td><td></td></tr><tr><td>2</td><td>T --> ~R</td><td></td><td></td></tr><tr><td>:.</td><td>~T</td><td></td><td></td></tr><tr><td>3</td><td>~~R --> ~T</td><td>1</td><td>Transposition</td></tr><tr><td>4</td><td>R --> ~T</td><td>3</td><td>Double Negation</td></tr><tr><td>5</td><td>T --> ~T</td><td>1, 4</td><td>Hypothetical Syllogism</td></tr><tr><td>6</td><td>~T v ~T</td><td>5</td><td>Material Implication</td></tr><tr><td>7</td><td>~T</td><td>6</td><td>Tautology</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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