Question 1209011
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I'll use an arrow instead of a 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>W --> Z</td><td></td><td></td></tr><tr><td>2</td><td>W v Z</td><td></td><td></td></tr><tr><td>:.</td><td>Z</td><td></td><td></td></tr><tr><td>3</td><td>Z v W</td><td>2</td><td>Commutation</td></tr><tr><td>4</td><td>~(~Z) v W</td><td>3</td><td>Double Negation</td></tr><tr><td>5</td><td>~Z --> W</td><td>4</td><td>Material Implication</td></tr><tr><td>6</td><td>~Z --> Z</td><td>5, 1</td><td>Hypothetical Syllogism</td></tr><tr><td>7</td><td>~(~Z) v Z</td><td>6</td><td>Material Implication</td></tr><tr><td>8</td><td>Z v Z</td><td>7</td><td>Double Negation</td></tr><tr><td>9</td><td>Z</td><td>8</td><td>Tautology</td></tr></table>
Here's a list of <a href="https://www.algebra.com/algebra/homework/Conjunction/logic-rules-of-inference-and-replacement.lesson">rules of inference and replacement</a>
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