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On Z defined * by a ** b = a -b show tha...

On Z defined * by `a ** b = a -b` show that * is a binary operation of Z.

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Knowledge Check

  • Let G be subset of real numbers. For a,b, hat(I) G, define a**b=a+b-ab . Then ** is not a binary operation on the set of

    A
    natural numbers
    B
    integers
    C
    rational numbers
    D
    real numbers

    • Similar Questions

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    a ** b = a^(b) AA a, b in Z . Show that * is not a binary operation on Z by giving a counter example.

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    Let * be a binary operation on N defined by a ** b = HCF of a and b. Show that * is both commutative and associative.

    The operation * defined a**b = a . Is * a binary operation on z.

    An operation ** on Z^(**) (the set of all non-negative integers) is defined as a**b = a-b, AA a, b epsilon Z^(+) . Is ** binary operation on Z^(+) ?

    Let * be a binary operation on the set R defined by a ** b = (a + b)/2 . Show that * is commulative but not associative.

    An operation * on z^(+) ( the set of all non-negative integers) is defined as a * b = |quad a -b|, AA q,b in z^(+) .Is * a binary operation on z^(+) ?

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