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A binary operation * is defined on the s...

A binary operation * is defined on the set
`X=R-{-1}` by `x**y=x+y +xy, AA x, y in X`.
Check whether * is commutative and associative. Find its identity element and also find the inverse of each element of X.

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Let A=R xx R and be the binary operation on A defined by (a, b) *(c,d) = (a + c, b + d). Show that *is commutative and associative. Find the identity element for* on A, if any.

If A=N xx N and * is a binary operation on A defined by (a, b) ** (c, d)=(a+c, b+d) . Show that * is commutative and associative. Also, find identity element for * on A, if any.

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.

Let* be a binary operation on Q, defined by a*b= (3ab)/(5) .Show that is commutative as well as associative. Also, find its identity, if it exists.

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Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R = {(x,y):y is divisible by x} is reflexive, symmetric and transitive.

Constract the composition table/multiplication table for the binary operation * defined on {0,1,2,3,4}by a**b =axxb ("mod" =5) . Find the identity element if any. Also find the inverse elements of 2 and 4.

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MODERN PUBLICATION-TEST PAPER 5-PROBLEM
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  2. Show that the relation R is in the set A={1,2,3,4,5} given by R={(a, b...

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  3. A binary operation * is defined on the set X=R-{-1} by x**y=x+y +xy,...

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  4. Let f, g: R rarr R defined by f(x) = |x| + x, g(x) = |x|-x for all x i...

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  5. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  6. An animal feed company must produce 200kg of a mixture consisting of i...

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  7. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  8. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  9. Find the inverse of the following matrices using elementary transforma...

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  10. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  11. Express as a sum of a symmetric and a skew symmetric matrix: [[2,-1,3]...

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  12. If y=In(x^2 +y^2),then find dy/dx.

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  13. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  14. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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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. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  17. Evaluate int0^2abs(x^2+2x-3)dx

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  18. solve:ydx-xdy=xydx

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  19. int(xe^x)/(1+x^2)dx

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  20. int0^pi(xdx)/(1+sinx)

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