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9. Let A = {1,2,3,4,5,6). How many different relations are there on the set A? Consider the suboet A (RR) (P) - What femtial relation. to this? Explaise. 11. Given a finite set A, how many different relations are there on A?

9. Let A = {1,2,3,4,5,6). How many different relations are there on the set A? Consider the suboet A (RR) (P) - What femtial relation. to this? Explaise. 11. Given a finite set A, how many different relations are there on A?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. **Let \( A = \{1, 2, 3, 4, 5, 6\} \). How many different relations are there on the set \( A \)?** 11. **Given a finite set \( A \), how many different relations are there on \( A \)?** In the following exercises, subsets \( R \) of \( \mathbb{R}^2 = \mathbb{R} \times \mathbb{R} \) or \( \mathbb{Z}^2 = \mathbb{Z} \times \mathbb{Z} \) are indicated by gray shading. In each case, \( R \) is a familiar relation on \( \mathbb{R} \) or \( \mathbb{Z} \). State it. **12.** Diagram shows the xy-plane with the region below the line \( y = x \) shaded (indicating all points \( (x, y) \) where \( y \leq x \)) and labeled as \( R \). **13.** Diagram shows the xy-plane with the region to the left of the line \( x = y \) shaded (indicating all points \( (x, y) \) where \( x \leq y \)) and labeled as \( R \). **14.** Diagram shows a grid with dots. The area on or above the line \( y = x \) is shaded (indicating all integer-coordinate points \( (x, y) \) where \( y \geq x \)). **15.** Diagram shows a grid with dots. The area to the left of the line \( x = y \) is shaded (indicating all integer-coordinate points \( (x, y) \) where \( x \geq y \)).
Transcribed Image Text:9. **Let \( A = \{1, 2, 3, 4, 5, 6\} \). How many different relations are there on the set \( A \)?** 11. **Given a finite set \( A \), how many different relations are there on \( A \)?** In the following exercises, subsets \( R \) of \( \mathbb{R}^2 = \mathbb{R} \times \mathbb{R} \) or \( \mathbb{Z}^2 = \mathbb{Z} \times \mathbb{Z} \) are indicated by gray shading. In each case, \( R \) is a familiar relation on \( \mathbb{R} \) or \( \mathbb{Z} \). State it. **12.** Diagram shows the xy-plane with the region below the line \( y = x \) shaded (indicating all points \( (x, y) \) where \( y \leq x \)) and labeled as \( R \). **13.** Diagram shows the xy-plane with the region to the left of the line \( x = y \) shaded (indicating all points \( (x, y) \) where \( x \leq y \)) and labeled as \( R \). **14.** Diagram shows a grid with dots. The area on or above the line \( y = x \) is shaded (indicating all integer-coordinate points \( (x, y) \) where \( y \geq x \)). **15.** Diagram shows a grid with dots. The area to the left of the line \( x = y \) is shaded (indicating all integer-coordinate points \( (x, y) \) where \( x \geq y \)).
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