Gdtyjr

It was hard for me to come up with a title for this question. So, for one, my document is starting on the second page. The second issue is that I cannot seem to get everything to appear in my document. I have ten questions, but only 8 and part of the 9th show up. When I remove questions, the 10th one partially shows up. It's as if the entire document is trying to force itself all onto one page. Any help would be greatly appreciated. The code is below. I'm stumped. Thank you so much.

documentclass[a4paper, 12pt]article
usepackageamsmath,amsthm,amssymb,amsfonts, enumitem, fancyhdr, color, comment, graphicx, environ
newcommandpowerset[1]mathbbP(#1)
setcountersecnumdepth-2
usepackageparskip
usepackagetikz
setlengthparindent15pt

begindocument

sectionfbox1 textnormalLet emphA = 1, 2, 3. How many relations are there on A?


sectionfbox2 textnormalLet emphR be a relation from sets emphA to emphB. Prove that Rng($R^-1$) = Dom(R).


sectionfbox3 textnormalLet emphA = a, b, 1, 2, 3. Define emphR = (1, 1), (a, a), (a, b), (1, 2), (2, 1), (a, 1), (a, 2). Is this relation reflexive, symmetric, transitive, irreflexive, and/or antisymmetric? Explain. Draw a digraph of emphR.


sectionfbox4 textnormalLet emphA = a, b, 1, 2, 3. Let emphT be an equivalence relation on emphA such that aT2 and bT3. How many equivalence classes of emphT are possible? List the equivalence classes for all possibilities.


sectionfbox5 textnormalLet emphQ = (x, y) $in mathbbR times mathbbR$ : $. Is the relation emphQ reflexive, symmetric, transitive, irreflexive, and/or antisymmetric? Prove or disprove that each property holds.


sectionfbox6 textnormalProve that the collection $A_t$ : $t in [0, 1)$, where each of $A_t$ = z + t : $z in mathbbZ$ is a partition of $mathbbR$.


sectionfbox7 textnormalWrite the addition and multiplication tables for $mathbbZ_6$, the set of equivalence classes for the relation $equiv$ (mod 6).


sectionfbox8 textnormalDefine a relation $leq$ on all words by agreeing that one word is $<$ another if an only if the first word comes before the second when arranged in alphabetical order. Show that this relation, called the emphlexicographic order, is a total order. (If you don't know why this order is called lexicographic, look up the definition of this word in a emphlexicon).


section{fbox9 textnormalDraw the Hasse diagram for the poset 2, 3, 2, 3, 4, 5, 2, 3 , 4, 4, 5, 6 ordered by set inclusion.


sectionfbox10 textnormalLet emphA be a set and $subset$ be the ordering for emphP(emphA). Let emphB be a family of subsets of emphA. Prove that the least upper bound of emphB is $bigcup_XinemphBX$ and the greatest lower bound of emphB is $bigcap_XinemphBX$

enddocument