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4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants and F is the set of all frogs, and is a relation on A defined by ab if and only if a can jump over b. Write in mathematical notation with quantifiers: "Any two frogs that can both jump over the same elephant can also jump over each other." Write in words: "Vxe A, (3ye E,yox) ⇒ x€ F." Explain in words what it would mean for to be transitive.

4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants and F is the set of all frogs, and is a relation on A defined by ab if and only if a can jump over b. Write in mathematical notation with quantifiers: "Any two frogs that can both jump over the same elephant can also jump over each other." Write in words: "Vxe A, (3ye E,yox) ⇒ x€ F." Explain in words what it would mean for to be transitive.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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4 Elephants and frogs In this problem, A is the set of all animals, E is the set of all elephants and F is the set of all frogs, and is a relation on A defined by ab if and only if a can jump over b. Write in mathematical notation with quantifiers: "Any two frogs that can both jump over the same elephant can also jump over each other." Write in words: "Vxe A, (3ye E,yox) ⇒ x € F." Explain in words what it would mean for to be transitive.
Transcribed Image Text:4 Elephants and frogs In this problem, A is the set of all animals, E is the set of all elephants and F is the set of all frogs, and is a relation on A defined by ab if and only if a can jump over b. Write in mathematical notation with quantifiers: "Any two frogs that can both jump over the same elephant can also jump over each other." Write in words: "Vxe A, (3ye E,yox) ⇒ x € F." Explain in words what it would mean for to be transitive.
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