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State whether the following statements a...

State whether the following statements are true or false. Justify
If `**` is a commutative binary operation on N, then `a**(b**c)=(c**b)**a`

Text Solution

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`a**(b**c)=a**(c**b)=(c**b)**a,`
for all `a,b,c in N`
`therefore ` The given statement is true
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A N EXCEL PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Consider an operation ** defined on the set A={1,2,4,8} by a**b=LCM ...

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  2. Let ast be a binary operation on N defined by aastb=HCF of a and b I...

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  3. Let ** be a binary operation on the set Q of rational numbers as follo...

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  4. Let ** be a binary operation on the set Q of rational numbers as follo...

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  5. Let ** be a binary operation on the set Q of rational numbers as follo...

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  6. Let ** be a binary operation on the set Q of rational numbers as follo...

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  7. Consider the binary operation ast on the set R of real numbers, define...

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  8. Determine whether or not each of the definitions of ** given below giv...

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  9. Find which of the following of the operations given above has identity...

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  10. Find which of the following of the operations given above has identity...

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  11. Find which of the following of the operations given above has identity...

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  12. Find which of the following of the operations given above has identity...

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  13. Let ** be a binary operation on the set Z of integers as a**b=a+b+1. T...

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  14. Let A=NtimesN and ast be a binary operation on A defined by (a,b)...

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  15. State whether the following statements are true or false. Justify For...

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  16. State whether the following statements are true or false. Justify If ...

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  17. Consider a binary operation ** on N defined as a**b=a^3+b^3. Choose th...

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  18. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

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  19. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 if...

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  20. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

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