Question

Given that a= -10 , b=7 and c= -3 , verify that additional is commutative and associative . Also show that subtraction is nether commutative nor aassociative.

Answer 1

Step-by-step explanation:

Commutative Property of addition is :- a + b = b + a  -------(1)

But since there are 3 numbers we can add 2 more equations,

b + c = c + b  -------(2)

a + c  = c + a.  -------(3)

If you substitute the values of all the equations you get the same answer on both the sides, that is:-

From (1) ->  -10 + 7 = 7 - 10 = -3

From (2) ->  7 - 3 = -3 + 7 = 4

From (3) ->  -10 + -3 = -3 + -10 = -13

So by the given set of numbers , (-10 + 7) - 3 = -10 + (7 - 3)

So we can say that addition is commutative.

Similarly, Associative Property of addition is :- (a + b) + c = a + (b + c)

So by the given set of numbers , (-10 + 7) - 3 = -10 + (7 - 3) = -6

So we can say that addition is Associative .

But in case of subtraction,

By Commutative property :-

-10 - (7) $\neq$  7 - (-10)        {a - b $\neq$ b - a}

And by associative property,

(-10 + 7) - 3 $\neq$ -10 - (7 - 3)

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