a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this equivalence relation to partition the set {2, 4, 5, 6, 9, 23, 24, 31, 37} into equivalence classes.

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a. The relation x = y if and only if x mod 4 ==
y mod 4 is an equivalence relation. Use this
equivalence relation to partition the set {2, 4,
5, 6, 9, 23, 24, 31, 37} into equivalence
classes.
b. How many substrings "aab" are there in
wwkw, where w = aabbaab?
%3D
c. Prove that (L®)* = (L*)R for all languages L.
Transcribed Image Text:a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this equivalence relation to partition the set {2, 4, 5, 6, 9, 23, 24, 31, 37} into equivalence classes. b. How many substrings "aab" are there in wwkw, where w = aabbaab? %3D c. Prove that (L®)* = (L*)R for all languages L.
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