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Let A=Set of all real numbes except 1. L...

Let A=Set of all real numbes except 1. Let * be defined as
`a+b-ab` for all `a, b in A`.Show that * is associative

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Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab for all a, b in A .Show that 0 is the identity element w.r.t. cdot .

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Consider the operations '*' and o+ on the set R of all real numbers defined as a* b = |a-b| and a o+ b = a for all a, b in R. Prove that o+ is associative but n ot commutative.

Consider the operations '*' and o+ on the set R of all real numbers defined as a* b = |a-b| and a o+ b = a for all a, b in R. Prove that '*' is commutative but not associative.

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Let S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b in S. Prove that the given operation is : (I) commutative (II) associative.

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PRADEEP PUBLICATION-MODEL PAPER (2)-EXERCISE
  1. Evaluate: underset0overset(pi//2)int log(sinx)dx

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  2. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  3. Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for...

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  4. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  5. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  6. Prove that cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 3

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  7. Solve the following equations sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1

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  8. Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cr...

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  9. Find dy/dx if x^y + y^x = a^b

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  10. If f(x)={((x-5)/(|x-5|)+a" , if "xlt5),(a+b" , if "x=5),((x-...

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  11. Find the interval of increase and decrease of the function f(x)=log(1+...

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  12. Prove that the curves x=y^2 and xy=k cut at right angles* if 8k^2 =1

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  13. int (sin^-1x)/(1-x^2)^(3//2) dx

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  14. Evaluate: underset0 oversetpi int sinxdx .

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  15. Sketch the graph of the function: y=f(x)={(x, if, 0lexle1),(1/x, if, 1...

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  16. Solve the differential equation (d^2y)/(dx^2)=x+sinx given that when x...

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  17. There is a group of 50 people who are patriotic out of which 20 believ...

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  18. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

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  19. Experiments show that radium decomposes at a rate proportioanl to the ...

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  20. The following matrix depicts the number of students of a school who we...

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