Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. 3. Given: If a number is divisible by 4, then the number is divisible by 2. 12 is divisible by four. Conclusion: 12 is divisible by 2. SOLUTION: If p → q is a true statement and p is true, then q. Here, a number divisible 4 is divisible by 2 also and 12 is divisible by 4. So, 12 is divisible by 2 is a valid statement by the Law of Detachment. ANSWER: valid; Law of Detachment 4. Given: If Elan stays up late, he will be tired the next day. Elan is tired. Conclusion: Elan stayed up late. SOLUTION: If p is true, then q is true, but q being true does not necessarily mean that p is true. Elan could be tired because he worked out. So, the statement is invalid. ANSWER: Invalid; Elan could be tired because he worked out. eSolutions Manual - Powered by Cognero
All others did not satisfy the inequality simultaneously except #4 and #6 For #4: 2 < 5(1) + 2 i.e. 2 < 7 (true) 2 >= 1/2(1) + 1 i.e. 2 >= 3/2 (true) For #6 2 < 5(2) + 2 i.e. 2 < 12 (true) 2 >= 1/2(2) + 1 i.e. 2 >= 2
