Question

Which of the following statements is not true?(A) Both addition and multiplication are associative for whole numbers.(B) Zero is the identity for muliplication of whole numbers.(C) Addition and multiplication both are commutative for whole numbers.(D) Multiplication is distributive over addition for whole numbers.

Answer 1

(A)Both addition and multiplication are associative for whole numbers - TRUE

 { associative property = property in which different grouping also gives the same answer. (a+b)+c = a+(b+c) / (ab)c=a(bc) }

proof for addition-
(2+3)+5 = 2+(3+5)
    (5)+5 = 2+(8)                               {(a+b)+c  = a+(b+c)}
        10 = 10

proof for multiplication-
(2*3)5 = 2(3*5)
   (6)5 = 2(15)                                 {(ab)c = a(bc)}
     30 = 30

∴proved : Both addition and multiplication are associative for whole numbers 

(B)Zero is the identity for multiplication of whole numbers - FALSE

{identity- property in which when we get back the same number back(quotient)}
in addition and subtraction, additive identity is 0(zero) as when its subtracted or added you get back the same answer.it's only 0 as taking any other number would change its value.
proof-
2+0 = 2                 {addition}          [with 0]
2+1 = 3                                          [with 1(other no.)]
                   
2-0 = 2                  {subtraction}     [with 0]
2-1 = 1                                           [with 1(other no.)]

and in division and multiplication, indentity is always 1 as when the number gets multiplied or divided, you get back the same number.taking other number would result in change in the number's value.

proof-
2*1 = 2              {multiplication}          [with 1]
2*0 = 0                                               [with 0]
2*2 = 4                                               [with 2]
                                  
2/1 = 2              {division}                   [with 1]
2/0 = 0                                               [with 1]
2/2 = 1                                               [with 1]

∴Zero is the identity for addition and subtraction rather multiplication and division of whole numbers.

(C)Addition and multiplication both are commutative for whole numbers.- TRUE
(D) Multiplication is distributive over addition for whole numbers.TRUE

Answer 2

Answer:

the not true answer is option B