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State true or false with reason. “The op...

State true or false with reason. “The operation`ast`defined by `aastb=sqrt(a^2+b^2)` on `Q^(+)`” is a binary operation.

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Show that * On R defined by a*b = a +4 b^(2) is a binary operation or not.

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Determine whether a**b=sqrt(a^2+b^2) on Q_+ operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. Find least non negative integer r such that 1237"(mod 4)"+985"(mod 4)"...

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  2. Find least positive integer x, satisfying 276x+128=4 (mod 7).

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  3. State true or false with reason. “The operationastdefined by aastb=sqr...

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  4. What does the solution set of the inequation 2x+ygt5 represents?

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  5. If sin^(-1)frac[x][5]+cosec^(-1)frac[5][4]=frac[pi][2], then what is t...

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  6. What is the value of sin(tan^(-1)x+tan^(-1)frac[1][x]),xgt0 ?

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  7. Express each of e^x function as the sum of an even function and an odd...

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  8. Express each of x^2 function as the sum of an even function and an odd...

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  9. Let f(x)={(1, x in Q), (0, x in R-Q):} and g(x)={(1, x in R-Q), (0, x ...

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  10. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  11. Determine if the binaary operation o on the set R of real numbers defi...

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  12. On the set R of real numbers, a binary operation o is defined by a0b=a...

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  13. Find the idenity and inverse if any for the binary operation ** on Q-{...

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  14. Find the identity elements if any for the binary operations defined by...

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  15. Find the identity elements if any for the binary operations defined by...

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  16. Let f:Rto(-1,1) be defined by f(x)=x/(1+x^2),x in R. Find f^(-1) if ex...

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  17. Show that AxxA is an equivalence relation on a non-empty set A. What i...

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  18. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  19. Let R be the relation on Z defined by aRb iff a-b is an even integer. ...

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  20. Prove that cos tan^(-1)sin cot^(-1)x=sqrt((1+x^2)/(2+x^2).

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