Question

1.2.1. Write each of the following explicitly. (a) {1} × {1, 2} × {1, 2, 3} (b) ? × {1, 2} (c) 2^{1, 2} × {1, 2} 1.2.2. Let R = {(a, b), (a, c), (c, d), (a, a), (b, a)}. What is R ? R, the composition of R with itself? What is R?¹, the inverse of R? Is R, R ? R, or R?¹ a function?

          1.2.1. Write each of the following explicitly.
(a) {1} × {1, 2} × {1, 2, 3}
(b) ? × {1, 2}
(c) 2^{1, 2} × {1, 2}

1.2.2. Let R = {(a, b), (a, c), (c, d), (a, a), (b, a)}. What is R ? R, the composition of R with itself? What is R?¹, the inverse of R? Is R, R ? R, or R?¹ a function?

1.2.1. Write each of the following explicitly.
(a) 1 × 1, 2 × 1, 2, 3
(b) ? × 1, 2
(c) 2^1, 2 × 1, 2

1.2.2. Let R = (a, b), (a, c), (c, d), (a, a), (b, a). What is R ? R, the composition of R with itself? What is R?¹, the inverse of R? Is R, R ? R, or R?¹ a function?

Added by Janice W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/07/2023

Step 1

2.1. Write each of the following explicitly: {1} x {1,2} x {1,2,3}: This is a Cartesian product of three sets. We can write it as: $\{(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3)\}$ 0 x {1,2}: This is an empty set, since 0 is not a set. We can write it Show more…

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1.2.1. Write each of the following explicitly. (a) {1} × {1, 2} × {1, 2, 3} (b) ∅ × {1, 2} (c) 2^{1, 2} × {1, 2} 1.2.2. Let R = {(a, b), (a, c), (c, d), (a, a), (b, a)}. What is R ∘ R, the composition of R with itself? What is R⁻¹, the inverse of R? Is R, R ∘ R, or R⁻¹ a function?