/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Let \(A=\\{3,4,5\\}\) and \(B=\\... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 17

Let \(A=\\{3,4,5\\}\) and \(B=\\{4,5,6\\}\) and let \(R\) be the "less than" relation. That is, For all \((x, y) \in A \times B, \quad x R y \Leftrightarrow x

Short Answer

Expert verified
The ordered pairs of the "less than" relation R are: R = {(3, 4), (3, 5), (3, 6), (4, 5), (4, 6)} And the ordered pairs of R^{-1} are: R^{-1} = {(4, 3), (5, 3), (6, 3), (5, 4), (6, 4)}

Step by step solution

01

List all ordered pairs in A 脳 B

To find the ordered pairs, we will combine every element of A with every element of B: A = {3, 4, 5} and B = {4, 5, 6} A 脳 B = {(3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6)}
02

Determine the ordered pairs in R (less than relation)

Now we will identify the ordered pairs in R based on the "less than" relation: For each ordered pair (x, y) in A 脳 B, x R y if x < y. So, R = {(3, 4), (3, 5), (3, 6), (4, 5), (4, 6)}
03

Determine the ordered pairs in R^{-1} (inverse of less than relation)

To find the ordered pairs in R^{-1}, we will swap the values of x and y from the pairs in R: For each ordered pairs (x, y) in R: (x, y) 鈭� R : R^{-1} = {(y, x)} So, R^{-1} = {(4, 3), (5, 3), (6, 3), (5, 4), (6, 4)}
04

Conclusion

The ordered pairs of the "less than" relation R are: R = {(3, 4), (3, 5), (3, 6), (4, 5), (4, 6)} And the ordered pairs of R^{-1} are: R^{-1} = {(4, 3), (5, 3), (6, 3), (5, 4), (6, 4)}

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