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Give an example of a relation which is t...

Give an example of a relation which is transitive but neither reflexive nor symmetric.

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To provide a step-by-step solution to the question, we will define the terms involved, create a suitable set and relation, and then verify the properties of the relation. ### Step 1: Define the Properties of Relations 1. **Reflexive Relation**: A relation R on a set A is reflexive if for every element a in A, the pair (a, a) is in R. 2. **Symmetric Relation**: A relation R on a set A is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R. 3. **Transitive Relation**: A relation R on a set A is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in R. ### Step 2: Define a Set ...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Give an example of a relation which is symmetric and transitive but...

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  2. Give an example of a relation which is symmetric but neither reflex...

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  3. Give an example of a relation which is transitive but neither refle...

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  4. Given the relation R={(1,\ 2),\ (2,\ 3)} on the set A={1,\ 2,\ 3} , ad...

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  5. Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (1,\ 1),\ (2,\ 3)} be a relation on...

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  6. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  7. Each of the following defines a relation on N : (i)x > y ...

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  8. Let R be a relation on the set of all lines in a plane defined by (l...

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  9. Show that the relation ‘is congruent to’ on the set of all triangle...

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  10. Show that the relation R defined on the set A of all triangles in a pl...

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  11. Let n be a positive integer. Prove that the relation R on the set Z o...

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  12. Show that the relation R on the set A of all the books in a library of...

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  13. Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...

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  14. Show that the relation R on the set A={x in Z :0lt=xlt=12} , given by...

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  15. Show that the relation R on the set A of points in a plane, given by R...

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  16. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ <=>(c ...

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  17. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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  18. Let N be the set of all natural numbers and let R be a relation on Nxx...

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  19. Let N denote the set of all natural numbers and R be the relation on ...

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  20. Prove that the relation congruence modulo m on the set Z of all int...

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