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Show that the relation `R` defined on the set `A` of all triangles in a plane as `R={(T_1,\ T_2): T_1` is similar to `T_2)` is an equivalence relation. Consider three right angle triangle `T_1` with sides `3,\ 4,\ 5;` `T_2` with sides `5,\ 12 ,\ 13` and `T_3` with sides 6, 8, 10. Which triangles among `T_1,\ T_2` and `T_3` are related?

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RD SHARMA ENGLISH-RELATIONS-All Questions
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  2. Show that the relation ‘is congruent to’ on the set of all triangle...

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

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

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

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

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

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

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  9. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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

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

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

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

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  14. Show that the number of equivalence relations on the set {1, 2, 3} ...

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  15. Given a non-empty set X , consider P\ (X) which is the set of all subs...

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  16. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

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  17. On the set N of all natural numbers, a relation R is defined as follow...

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  18. Show that the relation R defined by R={(a , b):a-b is divisible ...

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  19. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  20. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

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