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Show that zero is the identity for addit...

Show that zero is the identity for addition on R and 1 is the identity for multiplication on `R`. But there is no identity element for the operations. `- : R xx R rarr R` and `-:: R. xx R_. rarr R_.`

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that addition and multiplication are associativé binary operation...

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  2. Show that * :R xx R rarr R given by a* b= a+2 b is not associative.

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  3. Show that zero is the identity for addition on R and 1 is the identity...

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  4. Show that - a is not the inverse of a in N for the addition operation ...

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  5. Determine whether or not each of the definitions of ** given below giv...

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  6. For each binary operation ** defined below, determine whether ** is co...

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  7. Consider the binary operation on a set {1,2,3,4,5}. defined by a ^^ b=...

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  8. Consider the binary operation ** on the set A= {1,2,3,4,5} given by th...

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  9. Let **' be the binary operation on N given by a**'b= L.c.m. of a and b...

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  10. Consider an operation ** defined on the set A={1,2,4,8} by a**b=LCM ...

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  11. Let ast be a binary operation on N defined by aastb=HCF of a and b I...

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  12. Let ** be a binary operation on the set Q of rational numbers as follo...

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  13. Let A=NtimesN and ast be a binary operation on A defined by (a,b)...

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  14. State whether the following statements are true or false. Justify For...

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  15. Consider a binary operation ** on N defined as a**b=a^3+b^3. Choose th...

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  16. If R1 and R2 are equivalence relations in a set A, show that R1 nn R2 ...

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  17. Let X={1,2,3,4,5,6,7,8,9}. Let R1 be a relation in X given by R1={(x, ...

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  18. Let f: X rarr Y, be a function. Define a relation R in X given by: R={...

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  19. Determine which of the following binary operation on the set R are ass...

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  20. Find the number of all one-one functions from set A={1,2,3} to itself.

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