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Find the identity elements if any for the binary operations defined by `a**b=a+b+1,a,b inZ`.

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Find the identity elements if any for the binary operations defined by a**b=a+b+ab,a,b inQ-{-1} .

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Let be a binary operation defined by a*b = 7a+9b. Find 3*4.

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For each binary operation * defined below, determine the identity element. On Q^(+) , all positive rational numbers defined by a*b= (ab)/(2) .

On the set R of real numbers, a binary operation o is defined by a0b=a+b+a^2b AA a, b inR . Prove that the operation is neither commutative nor associative.

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. On the set R of real numbers, a binary operation o is defined by a0b=a...

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

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

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

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

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

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

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

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  10. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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  11. Prove that 2tan^-1(cosectan^-1x-tancot^-1x=tan^-1x.

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

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  13. If cos^-1x+cos^-1y+cos^-1z=pi, prove that x^2+y^2+z^2+2xyz=1.

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  14. Slove: tan(cos^-1x)=sin(cot^-1""1/2)

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  15. Find the feasible region of the inequations x+2ylt8, 2x+ylt8 and xgt0,...

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  16. Find the feasible region of the inequations 2x1+4x2gt40, 3x1+2x2gt60, ...

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  17. Shade the feasible region satisfying ineuations x1+2x2ge10, 2x1+2x2ge1...

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  18. Shade the feasible region satisfying ineuations x+2yle10, x+yge1, x-yl...

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  19. Shade the feasible region satisfying ineuations 4x+3yle60, 2x-yle0, x-...

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  20. Prove that the following sets A,B,C D are equivalent. WhereA={1,2,3,4,...

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