Question

which of the following properties is not satisfied by the whole numbers under multiplication?1....closure.2....associative.3....commutative..4......none of this.

Answer 1

4.. none of these

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Answer 2

Concept:

To answer this question, we need to first recall the following properties under multiplication (·) :

    1.  Closure property : "Product of any two real number is again a real

        number."

        for any a , b ∈ R ⇒ a.b ∈ R.

     2. Associative property : "Product of any three numbers does not change

       with the change in grouping of terms."

        for any a , b , c ∈ R  ⇒ a. (b.c) = (a.b). c

    3. Commutative property : "Product of  any two terms remain same after  

       reversing the terms."

       for any a , b ∈ R ⇒ a.b = b.a

Given:

The set of whole numbers under multiplication.

Solution:

A whole number are same as the natural numbers including 0 also.

A whole number under multiplication always  satisfy  :

closure property , associative property and commutative property.

Hence , option (4) is correct choice .