This should be so easy but I'm having trouble understanding why {{x},{x,y}} defines an ordered pair (x,y). I'm trying to work through the following problem from the Zakon Series pdf textbook:(adsbygoogle = window.adsbygoogle || []).push({});

I'm just learning to do formal proofs so not sure about where to start. Since it's an iff equivalence I assume that I need to show thatCode (Text):If (x,y) denotes the set {{x},{x,y}} [B]prove that, for any x, y, u, v,

we have (x,y) = (u,v) iff x=u and y=v[/B]. Treat this as a definition of an

ordered pair.

[Hint: Consider separately the two cases (x equals y) and

(x not equal to y), noting that {x,x}={x}]

1. if (x,y)=(u,v) then x=u and y=v

AND then also show that

2. if x=u and y=v then (x,y)=(u,v).

Is this the correct overall approach for proving the iff biconditional?

I'm OK with #2 since it's trivial to show that {{x},{x,y}}={{u},{u,v}} for x=u and y=v.

#1 also seems pretty simple when x=y but I'm not sure how to go about it for the case when x is not equal to y. Can you help me with this please.

Thank you,

Perion

[This isn't homework - I'm studying free math e-books on my own.]

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# Definition of ordered pair

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