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Activities 11.5 Activities
Activity 11.1 .
Develop an inductive definition of the set of words \(\words{\Sigma}\) from the alphabet \(\Sigma = \{ \mathrm{a},\mathrm{b},\mathrm{c} \}\text{.}\)
Then verify that the word \(\mathrm{ccababb}\) is in the set by tracing it back to the base clause.
Hint .
Steps:
Think of a simple way to form new words from old (inductive clause).
Then think about the basic words you need to get the process started (base clause).
Finally, decide whether you are certain you can form every possible word in a finite number steps starting at some base word.
Activity 11.2 .
Let \(\Sigma = \{\mathrm{a},\mathrm{z}\}\text{.}\) Write an inductive definition for the set of words in \(\words{\Sigma}\) that have the same number of \(\mathrm{a}\) letters as \(\mathrm{z}\) letters.
