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"If Jimmy takes the Math Class, Jimmy will lose his weight.
If Jimmy takes the Music Class, Jimmy will lose his hair.
Jimmy will take the Math Class and the Music Class.
Therefore, Jimmy will lose weight and hair."

Given these statements, I derived the proposition:

A: Jimmy takes the Math Class
B: Jimmy takes the Music Class
C: Jimmy will lose his weight
D: Jimmy will lose his hair

Hypothesis

A ⇒ C


Hypothesis

B ⇒ D


Hypothesis

A ∧ B


Modus Ponen 1,2,3

C ∧ D


Conclusion -> C ∧ D

I am unsure of my answer and so, I would like have some feedback on my solution.

J. Anderson
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    Not sure I understand the question. Clearly the claim "Therefore Jimmy will lose weight and hair" does not follow from the prior two statements. What, then, can "therefore" mean? – lulu Oct 23 '18 at 13:17
  • But there is no hypothesis $A\land B$ that is part of the original argument. (Unless you left it out.) We currently see no statement in the argument that in fact, Jimmy takes math class and music class. Hence, we can't use modus ponens, can we? And as lulu says, the conclusion does not follow from the premises/hypotheses. – amWhy Oct 23 '18 at 13:17
  • Sorry I missed the one sentence, I fill fix it – J. Anderson Oct 23 '18 at 13:18
  • Now, your argument is fine, except from $A\land B$, you need to simplify ($\land$-elimination), to get A separately, and B separately. Then use modus ponens twice. $A$ with $A\to C$ gives $C$. $B$ with $B\to D$ gives $D$. Then using $\land$-introduction on $C$, $D$, one derives $C \land D$. – amWhy Oct 23 '18 at 13:22
  • So, for simplification, A ∧ B -> A (conjunction elimination) is this the right approach for getting A? – J. Anderson Oct 23 '18 at 13:32
  • Yes (it depends on the rules you are working with; occasionally it is called simplification to derive $A$ from $A \land B$, as well as deriving $B$ from $A\land B$; other times it is justified as "conjunction elimination". They refer to the same rule of inference. – amWhy Oct 23 '18 at 16:32
  • I got it now, thank you for the help! – J. Anderson Oct 23 '18 at 16:48
  • J. Anderson. Why don't you answer your post? We like to have questions answered, and since you were very close in your work, why don't you take the suggestion about simplifying $A\land B$ to two derivations: A, B. And then use each, with the proper implication, and modus ponens, to get C, and then D. And then use "addition" or "conjunction-introduction" (whichever rule you've learned, to conclude $C\land D$, as desired? I'll be happy to confirm your answer. Then you can even accept your answer as correct. – amWhy Oct 23 '18 at 20:07

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