# In the set of all

(i) In the set of all rational numbers associativity in addition holds true

e.g.; A) let

Now a + (b + c) = (a + b) + c

LHS

RHS

LHS = RHS hence associativity holds true over addition in rational numbers

(ii) let us check for subtraction a –( b - c) = (a- b) - c

RHS

LHS

Hence associativity doesn’t hold true with subtraction in rational numbers

(ii) For two rational number addition and multiplication are commutative and subtraction and division are not commutative

e.g

And

But are not same hence commutate property is not true with division and subtraction

(iii) E.g

LHS =

RHS =

LHS = RHS

e.g

RHS

LHS

LHS = RHS

Hence the distributivity of multiplication over addition holds true for rational numbers

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