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Prove that the binary operation O define...

Prove that the binary operation O defined by `a o b = a-b+ab, AA a,b in Q` is not commutative and associative.

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Prove that the binary operation o defined by a o b = |a|+|b|, AA a,b in R is commutative and associatie on R.

Prove that the binary operation ** on RR defined by a**b=a+b+ab for all a,binRR is commutative and associative.

Prove that the binary operation @ defined on QQ by a@b=a-b+ab for all a,b in QQ is neither commutative nor associative.

The binary operation * define on N by a*b = a+b+ab for all a,binN is

Let A = N xx N and ** be the binary opertion on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative.

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Prove that the operation * an Z defined by a*b = a|b| for all a,b in Z is closed under*.

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UNITED BOOK HOUSE-SET 5-EXERCISE
  1. The equation of a plane parallel to z-axis is

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  2. A die thrown twice. If A is the event of getting a multiple of three i...

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  3. Prove that the binary operation O defined by a o b = a-b+ab, AA a,b in...

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  4. The value of tan^2 (sec^-1 2)+ cot^2(cosec^-1 3) is

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  5. Show that , A =1/3[[-1,2,-2],[-2,1,2],[2,2,1]] is proper orthogonal ma...

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  6. Without expanding show that |[27,40,58],[24,36,52],[18,28,40]|=0

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  7. If f(x)= {((tan 3x)/(4x),xne0 ),(k, x=0):}, then for what value of K, ...

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  8. lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0

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  9. Evaluate: int (x^2+1)/(x+1)^2 dx

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  10. Verify Rolle' theorem for the function f(x)= x^2-4x+3 in 1lexle3.

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  11. solve : (dy)/(dx) = (1-cos x)/(1+ cosx)

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  12. Find the interval in which the function f(x)= x^3-6x^2+9x+5 is decrea...

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  13. If vec a= 4 hati- hat j-3hat k and vec b = -2 hat i+hat j+2 hat k are ...

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  14. Find the equation of the plane passing through the point (4,1,1) and p...

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  15. The mean and standard deviationg of a binomial distribution B(n,p) ar...

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  16. The value 2tan^(-1)[sqrt((a-b)/(a+b))tan(theta/2)] is equal to cos^(-1...

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  17. If A = [[2,-1],[3,2]] and B = [[0,4],[-1,7]] then determine the matric...

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  18. If [1x1]xx[[1,3,2],[2,5,1],[15,3,2]]xx[[1],[2],[x]]=0 then find the va...

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  19. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  20. If y = 2 sin^(-1)(x-2)/sqrt6-sqrt(2+4x-x^2), then show that (dy)/(dx)|...

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