If Shane doesn't buy groceries, he will order take-out for dinner. Shane bought groceries. Therefore, Shane will not order take-out. Which statement is its conclusion? Shane didn't buy groceries Shane will order take-out Shane bought groceries If Shane doesn't buy groceries he will order take-out. Shane will not order take-out Which statements are its premises?Select all that apply. Shane didn't buy groceries Shane bought groceries Shane will order take-out Shane will not order take -out If Shane doesn't buy groceries , he will order take-out. How will we symbolize the premises and conclusion using the simple statements: p - Shane buys groceries q - Shane orders take-out square Premise 2:?

To analyze the argument, let's break it down:<br /><br />**Conclusion:**<br />The conclusion of the argument is "Shane will not order take-out."<br /><br />**Premises:**<br />The premises that support this conclusion are:<br />1. "If Shane doesn't buy groceries, he will order take-out."<br />2. "Shane bought groceries."<br /><br />Now, let's symbolize the premises and conclusion using the simple statements provided:<br /><br />- Let \( p \) represent "Shane buys groceries."<br />- Let \( q \) represent "Shane orders take-out."<br /><br />**Symbolizing the Premises:**<br /><br />1. The first premise "If Shane doesn't buy groceries, he will order take-out" can be symbolized as:<br /> \[<br /> \neg p \rightarrow q<br /> \]<br /> (This means if not \( p \), then \( q \).)<br /><br />2. The second premise "Shane bought groceries" can be symbolized as:<br /> \[<br /> p<br /> \]<br /><br />**Conclusion:**<br /><br />The conclusion "Shane will not order take-out" can be symbolized as:<br />\[<br />\neg q<br />\]<br /><br />In summary, the logical structure of the argument is:<br /><br />- Premise 1: \(\neg p \rightarrow q\)<br />- Premise 2: \(p\)<br />- Conclusion: \(\neg q\)<br /><br />This argument uses a form of reasoning known as modus tollens, where from \(\neg p \rightarrow q\) and \(p\), we conclude \(\neg q\).