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Number of binary opertions on the set `{a,b}` are

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The total number of binary operations on the set S={1,2} having 1 as the identity element is n . Find n .

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

Determine which of the following binary opertions on the set R are associative and which are commutative. (a) a **b =1 AA a, b in R (b) a **b = ((a +b))/( 2) AA a,b in R

Show that the number of binary opertions on {1,2} having 1 as identity and having 2 as the inverse of 2 is exactly one.

Let ** be a binary operation on NN , the set of natural numbers defined by a**b=a^(b) for all a,binNN is ** associative or commutative on NN ?

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Consider a binary opertion ** on the set {1,2,3,4,5} given by the following multiplication table (Table 1.2) (i) Compute (2 **3) **4 and 2 ** (3**4) (ii) Is ** commutative ? (iii) Compute (2 **3) ** (4 **5).

Let ** be a binary opertion on the set Q of rational numbers as follows: a ** b = (a-b) ^(2) commutative and associative.

Let @ be a binary operation on QQ , the set of rational numbers, defined by a@b=(1)/(8)ab for all a,binQQ . Prove that @ is commutive as well as associative.

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.

PATHFINDER-RELATIONS , FUNCTIONS AND BINARY OPERATIONS-QUESTION BANK
  1. Let f:RrarrR be a function defined by f(x)=cos(2x+3). Show that this f...

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  2. Let f(x)=(ax)/(x-1),x ne-1.If 10f(x)=x, find the value of a.

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  3. Let f be function defined on [0,1] defined by:f(x)={(x, if, x ,in, q),...

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  4. Find the domain and range of the following function :sqrt((x-1)(3-x))

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  5. If f(x)=sqrt(8x),g(x)=x+2, then

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  6. Let A=[-1,1] and f:ArarrA be a function defined by f(x) =xabsx. Show ...

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  7. Show that the function f:NrarrN defined by f(x)=x^2+x+1inNis not inve...

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  8. Let y={n^2:ninN}subeN. consider f: NrarrY as f(n)=n2. Show that is inv...

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  9. Let f :R R-{3/5}rarrR-{2/5} be a function defined as f (x)= (2x)/(5x+3...

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  10. Let A= {a+sqrt5b:a,binZ}. Show that usual multiplication of numbers is...

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  11. Let be binary operation on the set R defined by a*b = a+b+ab, a, binR....

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  12. Number of binary opertions on the set {a,b} are

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  13. Let * be a binary operation on N defined by a*b=2^(5ab),a b inN.Discus...

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  14. Let A=N x N and *be a binary operation on A defined by (a,b)*(c,d) =(a...

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  15. Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ.Show...

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  16. Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ. Sho...

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  17. Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ . Fi...

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  18. Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ Find...

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  19. Let A= Q xxQ. Let * be a binary operation Defined by: (a,b)*(c,d)= (ac...

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  20. Let A= Q xxQ. Let * be a binary operation Adifined by: (a,b)*(c,d)= (a...

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