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For each binary operation * defined belo...

For each binary operation * defined below, determine whether * is commutative or associative.(i) `O n Z , d efin e a*b = a - b`(ii) `O n Q , d efin e a*b = a b + 1`(iii) `O n Q , d efin e a*b =(a b)/2`(iv) `O

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The correct Answer is:
Neither commutative nor associative
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For each binary operation * defined below, determine whether * is commutative or associative. (i) On Z , define a ∗ b = a – b (ii) On Q , define a ∗ b = ab + 1 (iii) On Q , define a ∗ b = (ab)/(2) (iv) On Z^+ , define a ∗ b = 2^(ab) (v) On Z^+ , define a ∗ b = a^(b) (vi) On R – {– 1} , define a ∗ b = (a)/(b+1)

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For each binary operation '**' defined below, determine whether '**' is commutative and whether '**' is associative : (iv) On Q, define '**' by a**b=(ab)/(3)

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Determine whether or not each of the definition of given below gives a binary operation. In the event that * is not a binary operation, give justification for this. (i) On Z^+ , define ∗ by a ∗ b = a – b (ii) On Z^+ , define ∗ by a ∗ b = ab (iii) On R , define ∗ by a ∗ b = ab^2 (iv) On Z^+ , define ∗ by a ∗ b = |a – b| (v) On Z^+ , define ∗ by a ∗ b = a

MODERN PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE 1 (e) (Short Answer Type Questions)
  1. Determine whether or not each of the definition of '**' given below gi...

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  2. Show that the binary operation '**' defined from NxxNrarrN and given ...

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  3. For each binary operation * defined below, determine whether * is com...

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  4. For each binary operation '**' defined below, determine whether '**' i...

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  5. For each binary operation '**' defined below, determine whether '**' i...

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  6. For each binary operation '**' defined below, determine whether '**' i...

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  7. For each binary operation '**' defined below, determine whether '**' i...

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  8. For each binary operation '**' defined below, determine whether '**' i...

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  9. For each binary operation '**' defined below, determine whether '**' i...

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  10. Is *defined on the set {1, 2, 3, 4, 5} b y a * b = LdotCdotMdotof a a...

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  11. Let *be the binary operation on N given by a*b = LdotCdotMdotof a and...

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  12. Let * be a binary operation on N defined by a ** b = HCF of a and b. S...

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  13. If n(A) = p and n(B) = q, then the number of relations from set A to s...

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  14. (a) Let '**' be a binary operation defined on Q, the set of rational n...

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  15. If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3)} in A...

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  16. In the binary operation **: QxxQrarrQ is defined as : (i) a**b=a+b-a...

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  17. The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN i...

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  18. Discuss the commutativity and associativity of the binary operation * ...

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  19. Find the domain and range of the real function f(x) = x/(1-x^2)

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  20. Show that the operation '**' on Q - {1} defined by a**b=a+b-ab for...

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