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136 expressions as much as possible by applying the |
136 expressions as much as possible by applying the |
137 following 7 simplification rules: |
137 following 7 simplification rules: |
138 |
138 |
139 \begin{center} |
139 \begin{center} |
140 \begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}ll} |
140 \begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}ll} |
141 $r \cdot \varnothing$ & $\mapsto$ & $\varnothing$\\ |
141 $r \cdot \ZERO$ & $\mapsto$ & $\ZERO$\\ |
142 $\varnothing \cdot r$ & $\mapsto$ & $\varnothing$\\ |
142 $\ZERO \cdot r$ & $\mapsto$ & $\ZERO$\\ |
143 $r \cdot \epsilon$ & $\mapsto$ & $r$\\ |
143 $r \cdot \ONE$ & $\mapsto$ & $r$\\ |
144 $\epsilon \cdot r$ & $\mapsto$ & $r$\\ |
144 $\ONE \cdot r$ & $\mapsto$ & $r$\\ |
145 $r + \varnothing$ & $\mapsto$ & $r$\\ |
145 $r + \ZERO$ & $\mapsto$ & $r$\\ |
146 $\varnothing + r$ & $\mapsto$ & $r$\\ |
146 $\ZERO + r$ & $\mapsto$ & $r$\\ |
147 $r + r$ & $\mapsto$ & $r$\\ |
147 $r + r$ & $\mapsto$ & $r$\\ |
148 \end{tabular} |
148 \end{tabular} |
149 \end{center} |
149 \end{center} |
150 |
150 |
151 \noindent Write down your simplified derivative in a readable |
151 \noindent Write down your simplified derivative in a readable |