EDB — 01N

Exercises

1. [01N](Solved on 2022-10-25) Prerequisites:[1Y9]↺↻. The ordered pair is defined as

   \[ (x,y){\stackrel{.}{=}}\{ \{ x\} ,\{ x,y\} \} \quad ; \]

   (note that the axiom of pairing [1Y3]↺↻ guarantees us that this is a good definition); show that

   \begin{equation} (a,b)=(x,y) \iff (a=x\wedge b=y)\quad .\label{eq:identita_ coppia} \end{equation}

   51

   (First solution that doesn’t use [1Y9]↺↻)

   Solution 1

   [1WZ]↺↻

   )

   (Second solution using [1Y9]↺↻)

   Solution 2

   [1YC]↺↻

   )