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Problem 2

Avg difficulty 3.0

Let the sets

A\displaystyle A ={x∈R∣x2−x−2≤0} and\displaystyle=\{x\in\mathbb{R}\mid x^{2}-x-2\leq 0\}\text{ and} B\displaystyle B ={x∈[0,∞)∣12−x−x2>0}.\displaystyle=\{x\in[0,\infty)\mid 12-x-x^{2}>0\}.

  1. Express A∩BA\cap B in interval notation.

  2. Express A∪BA\cup B in interval notation.

  3. Express B∖AB\setminus A in interval notation.

  4. Is A∖B⊂[−1,0)A\setminus B\subset[-1,0)? Explain.

Kan, A Complete Introduction to Abstract Algebra, Preliminaries, Sets, Problem 2

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Adapted from A Complete Introduction to Abstract Algebra © 2022–2026 Kan Onn Kit. Licensed under CC BY-SA 4.0. Source: A Complete Introduction to Abstract Algebra. Imported at revision a559e8b.