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Show that *: R xx R rarr R defined by a ...

Show that *`: R xx R rarr R` defined by a * b`=a+2 b` is not commutative.

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

Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binary operaions, but - : R xx R rarr R and -:: R_* xx R_* rarr R_* are not commutative.

Show that f: R rarr R defined by f(x) = (x-1) (x-2) (x-3) is surjective but not injective

Show that * : R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binary operation.

Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and the * : R xx R rarr R given by (a, b) rarr min {a , b} are binary operations.

Show that the function f : R_** rarr R_** defined by f (x) = 1/x is one-one and onto,where R_** is the set of all non-zero real numbers. Is the result true, if the domain R_** is replaced by N with co-domain being same as R_** ?

Consider the binary operation ast on the set R of real numbers, defined by aastb=a b /4 Show that ast is commutative and associative.

*: RxxRrarr R is given by a**b=3a^2-b .Find the value of 2*3.Is * commutative?Justify your answer.

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and t...

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  2. Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binar...

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  3. Show that *: R xx R rarr R defined by a * b=a+2 b is not commutative.

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  4. Show that addition and multiplication are associativé binary operation...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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