The following expressions would be legitimate steps in a proof sequence:1. (∀x)[P(x) → Q(x)] hyp2. (∃ y)P( y) hyp3. P(a) 2, ei4. P(a) → Q(a) 1, ui5. Q(a) 3, 4, mpIn step 3, the specific element with property P was given the name a. In step 4, ui was then used to say that an implication that is universally true in the domain is certainly true for this a. Steps 3 and 4 cannot be reversed. If ui is first used on hypothesis 1 to name a constant a, there is then no reason to assume that this particular a is the one that is guaranteed by hypothesis 2 to have property P.
The following expressions would be legitimate steps in a proof sequence:1. (∀x)[P(x) → Q(x)] hyp2. (∃ y)P( y) hyp3. P(a) 2, ei4. P(a) → Q(a) 1, ui5. Q(a) 3, 4, mpIn step 3, the specific element with property P was given the name a. In step 4, ui was then used to say that an implication that is universally true in the domain is certainly true for this a. Steps 3 and 4 cannot be reversed. If ui is first used on hypothesis 1 to name a constant a, there is then no reason to assume that this particular a is the one that is guaranteed by hypothesis 2 to have property P.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following expressions would be legitimate steps in a proof sequence:
1. (∀x)[P(x) → Q(x)] hyp
2. (∃ y)P( y) hyp
3. P(a) 2, ei
4. P(a) → Q(a) 1, ui
5. Q(a) 3, 4, mp
In step 3, the specific element with property P was given the name a. In step 4, ui was then used to say that an implication that is universally true in the domain is certainly true for this a. Steps 3 and 4 cannot be reversed. If ui is first used on hypothesis 1 to name a constant a, there is then no reason to assume that this particular a is the one that is guaranteed by hypothesis 2 to have property P.
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