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Show that the vee: R xx R rarr R given b...

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.

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Sincę .vv. carries each pair .(a, b). ìn .R xx R. to a unique element namely maximum of .a. and .b. lying in .R, V. is a binary operation. Using the similar argument, one can say that .. is also a binary operation.
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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Show that *: R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binar...

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  2. Let P be the set of all subsets of a given set X. Show that uu: P xx P...

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  3. Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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