I'm really not understanding the set up of how to go about solving this problem any help is welcome
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1What is the meaning of the empty screenshot ? – Mauro ALLEGRANZA Nov 29 '18 at 19:00
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I'm really not understanding the set up of how to go about solving this problem any help is welcome .
Let us have a look. You have a definition of union of sets, and a definition of equality for sets. You need to show two unions are equal for some free terms a and b.
| [a,b] Free Terms (implicit)
| Ɐx Ɐy Ɐz (z ϵ Union(x,y) ↔ (z ϵ x ˅ z ϵ y)) Premise I (defines Union)
|_ Ɐx Ɐy (Ɐz (z ϵ x ↔ z ϵ y) → x = y) Premise II
| : :
| : :
| Union(a,b) = Union(b,a) Magic?
Okay... The first step is obviously to use Universal Elimination to instantiate to some terms.
Tip: If a and b are both terms, then Bivariate Functions Union(a,b) and Union(b,a) are also terms.
| [a,b] Free Terms
| Ɐx Ɐy Ɐz (z ϵ Union(x,y) ↔ (z ϵ x ˅ z ϵ y)) Premise I
|_ Ɐx Ɐy (Ɐz (z ϵ x ↔ z ϵ y) → x = y) Premise II
| Ɐy (Ɐz (z ϵ Union(a,b) ↔ z ϵ y) → Union(a,b) = y) Ɐ Elimination (of Premise II)
| Ɐz (z ϵ Union(a,b) ↔ z ϵ Union(b,a)) → Union(a,b) = Union(b,a) Ɐ Elimination (of above)
| : :
| : :
| Union(a,b) = Union(b,a) → Elimination ?
So... There you go. Take it away.
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Using some of what was previously shown above I was able to to make a similar outline and add a subproof to figure out the answer
