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Define a binary opeartion ** on a non-em...

Define a binary opeartion `**` on a non-empty set A.

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Knowledge Check

  • We define a binary relation ~ on the set of all 3 xx 3 real matrices as A ~ B if any there exist invertible matrices P and Q that B = PAQ^(-1) . The binary relation ~ is

    A
    neither reflexive nor symmetric
    B
    reflexive and symmetric but not transitive
    C
    symmetric and transitive but not reflexive
    D
    an equivalence relation

  • Let ** be a binary operation on NN , the set of natural numbers defined by a**b=a^(b) for all a,binNN is ** associative or commutative on NN ?

    A
    not commutative
    B
    associative
    C
    commutative
    D
    not associative

  • Number of binary opertions on the set {a,b} are

    A
    10
    B
    16
    C
    20
    D
    8

    • Similar Questions

    Explore conceptually related problems

    Let ** and @ be two binary operations on a non-empty setA. Then write the condition for which the binary operation ** is distibutive over binary operation @

    Prove that the identity element of the binary opeartion ** on RR defined by a**b = min. (a,b) for all a,binRR , does not exist.

    If the binary operation ** on the set ZZ is defined by a**b=a+b-5 , then the identity element with respect to ** is K . Find the value of K .

    We define a binary relation ~ on the set of all 3xx3 real matrices as A ~B if and only if these exist invertible matrices P and Q such that B= PAQ ^(-1) .The binary relation ~ is -

    The binary operation ** on the set A={1,2,3,4,5} is defined by a**b= maximum of a and b. Construct the composition table of the binary operation ** on A.

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