Let L be a regular language over {a, b, c}. Show that each of the following sets is regular. a)

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Step 1: Define the set $A u003D u005C{w u005Cmid w u005Ctext{ contains an } au005C}$. This set can be described by t

Let $\mathrm{L}$ be a regular language over $\{a, b, c\}$. Show that each of the following sets is regular. a) $\{w \mid w \in \mathrm{L}$ and $w$ contains an $a\}$ b) $\{w \mid w \in$ L or $w$ contains an $a\}$ c) $\{w \mid w \notin \mathrm{L}$ and $w$ does not contain an $a\}$