Homework4.tex

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\title{	
\normalfont \normalsize 
\textsc{San Francisco State University} \\ [25pt]
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\huge MATH 301 Assignment 4  \\ % The assignment title
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\author{Omar Sandoval}

\date{\normalsize\today}

\begin{document}

\maketitle

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%	PROBLEM 2
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\textbf{2.} By using a truth table prove that, for sets $A, B,$ and $C$,\\
$A \cup ( B \cap C ) = ( A \cup B ) \cap ( A \cup C )$ \\
Draw a Venn diagram to illustrate the proof. \\

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%	PROBLEM 4
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\textbf{4.} Prove by contradiction or otherwise that $A \cap B = B \cap C$ and $ A \cup B
 = A \cup C$ if and only if $B = C$. \\

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%	PROBLEM 5
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\textbf{5.} Using truth tables, prove that for sets A, B and C, \\
(i) $(A \cup C) - B \subset (A - B) \cup C$ \\
(ii) $(A \cap C) - B = (A - B) \cap C$ \\

Draw Venn diagrams to illustrate the proofs.
Prove that there is equality in the first of these results if and only if $B \cap C$
 $\not= \emptyset$. \\
Deduce from the second of these results that $(A-B)\cap C = \emptyset$ if and only if
 $A \cap C \subset B$.
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%	PROBLEM 7
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%	PROBLEM 12
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%	PROBLEM 13
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