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| Binary Operations |
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| Let S be any non-empty set. An operation * is called a binary
operation on S if " a, b Î
S a * b Î S |
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| Example: |
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| (1) '+' is a binary operation on the set of naturals. |
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| (2) '.' is a binary operation on the set of naturals. |
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| (iv) Addition, subtraction and multiplication are binary operations on I. |
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| Let * be a binary operation on the set S.
* is said to be associative in S if " a, b
Î S a * b = b * a |
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| Note: |
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| (1) '+' & '.' are commutative and associative in the sets, N, I, Q, Q|, R and C. |
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| i.e, a + b = b + a |
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| and a.b = b.a |
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| a + (b + c) = (a + b) + c |
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