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A binary operation * on the set {0,1,...

A binary operation * on the set {0,1,2,3,4,5} is defined as: `a*b={a+b a+b-6"\ \ \ \ if\ "a+b<6"\ \ \ if"\ a+bgeq6` Show that zero is the identity for this operation and each element a of the set is invertible with 6a, being the inverse of a.

A

0

B

1

C

2

D

3

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A
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Define a binary operation ** on the set A={0,1,2,3,4,5} as a**b=(a+b) \ (mod 6) . Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of a . OR A binary operation ** on the set {0,1,2,3,4,5} is defined as a**b={[a+b if a+b = 6]} Show that zero is the identity for this operation and each element a of the set is invertible with 6-a , being the inverse of a .

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Consider the binary operation* on the set {1, 2, 3, 4, 5} defined by a * b=min. {a, b}. Write the operation table of the operation *.

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

Consider the infimum binary operation ^^ on the set S={1,2,3,4,5} defined by a^^b= Minimum of aandb .Write the composition table of the operation ^^ .

Let *prime be the binary operation on the set {1," "2," "3," "4," "5} defined by a*primeb=" "HdotCdotFdot of a and b. Is the operation *prime same as the operation * defined in Exercise 4 above? Justify your answer.

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Define a binary operation * on the set A={1,2,3,4} as a*b=ab(mod5) show that 1 is the identity for * and all elements of the set A are invertible with 2^(-1)=3 and 4^(-1)=4

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DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)
  1. If f: R to R, g: R to R and h: R to R is such that f(x)=x^(2), g(x)= t...

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  2. Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sin...

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  3. If f(x)=1+x+x^2+x^3+....oo for |x| < 1 then f^-1(x)=

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  4. Let f be a function with domain X and range Y. Let A, B sube X and C, ...

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  5. If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...

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  6. A binary operation * on the set {0,1,2,3,4,5} is defined as: a*b={...

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  7. Let * be a binary operation on N given by a*b=H C F\ (a ,\ b),\ \ a...

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  8. Show that the total number of binary operation from set A to A is n^(n...

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  9. If fQ to Q f(x)=2x,g,Q to Q, g (x)=x+2 then value of (fog)^(-1)(20) is

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  10. If g(x)=x-2 is the inverse of the function f(x)=x+2, then graph of g(x...

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  11. Which of the following is not a binary operation on the indicated set?

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  12. If f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2, ...

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  13. Let f(x)=(ax+b)/(cx+d). Then the fof (x) =x provided that

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  14. Let A={1,2,3,4,5} and functions f:A to and g: A to A to defined by f(1...

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  15. Suppose that f is an even function, g is an odd function and both f an...

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  16. If f(x)=e^(x) and g(x)= log(e)x, hen which of the following is true?

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  17. The inverse of the function f(x)=(e^x-e^(-x))/(e^x+e^(-x))+2 is given ...

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  18. Show that if f: R-{7/5}->R-{3/5} is defined by f(x)=(3x+4)/(5x-7) a...

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  19. Let f:R to be defined by f(x)=3x^(2)-5 and g : R to R by g(x)=(x)/(x^...

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  20. Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

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