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For real numbers x and y, define x R y i...

For real numbers x and y, define x R y if and only if `x-y +sqrt(2)` is an irrational number. Is R transitive? Explain your answer.

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The correct Answer is:
No,(1,sqrt 3),(sqrt 3, sqrt 2)`in` R but (1,Sqrt 2)!`in` R
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MODERN PUBLICATION-TEST PAPER 6-EXERCISE
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  2. Find the least value of n for which tan^(-1)(n/π)>π/4,n varepsilon N i...

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  3. If matrix A=[{:(1,-1),(-1,1):}]andA^(2)=kA , then write the value of k...

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  4. IF |{:(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x):}| =a+bx+cx^2+dx^3+ex^4+fx^5...

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  5. If xin((3pi)/4,pi) what is dy/dxfor y = | cos x | + | sin x | ?

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  6. Give example of a function which is increasing in (-oo,2) and (3,oo) a...

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  7. What is the value of int e^(x)dx.

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  8. Write the solution of sqrt 3x+dy/dx=2.

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  9. Write the equation of the line passing through the points (3,-2,-5) an...

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  10. Find the volume of parallelopiped with edges 2vec i-3vec j ,vec i +vec...

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  11. Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b...

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  12. Consider f:R(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is in...

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  13. A merchant sells two models X and Y of TV with cost price ₹ 25000 and ...

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

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  15. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  16. Using determinants, find the values of a if the area of triangle with ...

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  17. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  18. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

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  19. Differentiate tan^-1((2x)/(1-x^2)).

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  20. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

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