/sci/ - Science & Math

I'm working through the book How to Prove It: A Structured Approach by Daniel Velleman. He only provides selected answers, so I'm coming here to ask about some work I've done on reducing these statements to logical connectives, quantifiers, and bound/unbound variables. I can't let any set notation or negations remain. How wrong am I?

Where <div class="math">A_i</div> and <div class="math">B_i</div> are indexed set families:
<div class="math">x \in \cap_{i \in I} (A_i \cup B_i) </div>
Is the same as
<div class="math">\forall x \exist i \in I (x \in A_i \or x \in B_i)
Is the same as
<div class="math">x \in \left ( \bigcap_{i \in I} A_i \cup \bigcap_{i \in I} B_i \right )</div>

Any discussion of interesting areas involving sets or their interaction with other fields of mathematics is welcome.</div>

When we do find life, extraterrestrial or otherwise, there's only one way to deal with it.

Also you jerks saying bad things about girls obviously haven't had sex or you'd have trained yourselves to kiss their ass like your detractors have done.

Everyone knows goddess-sisters never say stupid things like boys always do. It's biological or something.

ITT: Sagan