Give examples of languages L1 and L2 over {a, b} that satisfy the descriptions below. a) L1 is r

Step 1: **Understanding the problem**u000AWe need to find examples of languages u005C( u005Cmathrm{L}_1 u005C) a

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Give examples of languages $\mathrm{L}_1$ and $\mathrm{L}_2$ over $\{a, b\}$ that satisfy the descriptions below. a) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular. b) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is nonregular. c) $L_1$ is regular, $L_2$ is nonregular, and $L_1 \cap L_2$ is regular. d) $\mathrm{L}_1$ is nonregular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular. e) $L_1$ is nonregular and $L_1^*$ is regular.

    Give examples of languages $\mathrm{L}_1$ and $\mathrm{L}_2$ over $\{a, b\}$ that satisfy the descriptions below.
a) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular.
b) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is nonregular.
c) $L_1$ is regular, $L_2$ is nonregular, and $L_1 \cap L_2$ is regular.
d) $\mathrm{L}_1$ is nonregular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular.
e) $L_1$ is nonregular and $L_1^*$ is regular.

Languages and Machines: An Introduction to the Theory of Computer Science

Thomas A. Sudkamp 2nd Edition

Chapter 7, Problem 14

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Step 1: **Understanding the problem** We need to find examples of languages $ \mathrm{L}_1 $ and $ \mathrm{L}_2 $ over the alphabet \{a, b\} that satisfy specific conditions regarding their regularity and the regularity of their union and intersection. Show more…

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Give examples of languages $\mathrm{L}_1$ and $\mathrm{L}_2$ over $\{a, b\}$ that satisfy the descriptions below. a) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular. b) $\mathrm{L}_1$ is regular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is nonregular. c) $L_1$ is regular, $L_2$ is nonregular, and $L_1 \cap L_2$ is regular. d) $\mathrm{L}_1$ is nonregular, $\mathrm{L}_2$ is nonregular, and $\mathrm{L}_1 \cup \mathrm{L}_2$ is regular. e) $L_1$ is nonregular and $L_1^*$ is regular.

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