# In the set of all rational numbers, give 2 examples each illustrating the following properties:(i) associativity(ii) commutativity(iii) distributivity of multiplication over addition.

(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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