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Discuss the commutativity and associati...

Discuss the commutativity and associativity of binary operation .*. defined on A = Q - {1} by the rule `a**b=a-b+ab` for all `a, b in A`. Also, find the identity element of * in A and hence find the invertible elements of A.

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The correct Answer is:
So, .*. is not associative on Q.
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ARIHANT PRAKASHAN-VERY SIMILAR TEST 5-SECTION B
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  2. Discuss the commutativity and associativity of binary operation .*. d...

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  3. Directions (Q. Nos. 27 and 28) Solve the following equations: "tan"...

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  4. Answer any three questions (d) Solve the following LPP graphically M...

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  5. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  6. A die is rolled until a 6 is obtained. What is the probability that ...

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  7. Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}]andC=[{:(2,5),(3,8):}]. F...

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  8. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  9. The probability that A hits a target is 1/3 and the probability that B...

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  10. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

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  11. Verify Rolle.s theorem for the function f(x)=x^(2)-3x+2 in the interva...

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  12. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

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  13. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  14. Find (dy)/(dx), if y = k tan^(-1) ((y)/(x)).

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  15. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  16. Reduce x (dy)/(dx) + y = xy^(3) to linear differential equation.

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  17. Evaluate int [ (1)/( "In" x ) - (1)/(("In" x)^2) ]dx.

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  18. Find the differential equation for the family of curve y= a sin^(-1) x...

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  19. Solve (dy)/(dx) = e^("sin"^(-1) x). (sin^(-1) x)/( sqrt(1-x^(2) ).

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  20. Find the area bounded by the curve y=2 x -x^(2) and the straight line ...

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