Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Finally, note that there are no mistakes in format, phrasing, citations, or other aspects of presentation, so don't worry about that sort of thing. Just
Finally, note that there are no mistakes in format, phrasing, citations, or other aspects of presentation, so don't worry about that sort of thing. Just pay attention to what formulas are being used, what rules are being used, and what formula is being concluded. (a) Proof. 1. Assume (FG)G and F. 2. Since (FG)G is true, so is G. (V-Elim.) 3. From G, we can derive G. (Dbl. Neg.) 4. Because we have F and G, we can conclude FG. (^-Intro.) (b) Proof. 1. Assume AC and B. 2. Assume A. 3. From A and B, we get AB. (-Intro.) 4. Because A and AC, we can conclude C (Appl.) 5. Since C, we know C. (Dbl. Neg.) 6. Since we have AB and C, we know (AB)C (Dir. Pf.) (c) Proof. 1. Assume YZ and XY. 2. From YZ, we can derive Y and Z (^-Elim.) 3. Suppose towards a contradiction that X is true. 4. From X and XY, we get Y. (Appl.) 5. But Y contradicts our earlier statement Y. 6. Therefore X. (contrad.) 7. Suppose towards a contradiction that XZ is true. 8. Since XZ, we get X. (^-Elim.) 9. But X and X can't both be true. 10. Therefore we have (XZ). (contrad.) (d) Proof. 1. Assume YZ and XY. 2. Suppose towards a contradiction that X is true. 3. Because X and XY hold, so does Y. (Appl.) 4. Since YZ, we have Y and Z (^-Elim.) 5. From X and Z, we can conclude XZ ( -Intro.) 6. It's not possible to have both Y and Y. 7. From XZ, we proved a contradiction, and therefore (contrad.) (XZ)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started