If @ is an operation on integers such that a@b=a-b-2, for all integers a,b; then 7@(-4)=?
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Answer :
7*(-4) = 9
Note :
★ Binary Operation : When two elements are operated , then a new element is formed . If the new element belong to the same set to which the two given elements belongs , then the operation is called a binary operation .
★ An operation which has closure property is a binary operation .
★ A binary operation * on a set A is a function * : A×A → A .
★ We denote *(a,b) by a*b , where a,b € A
Solution :
★ Given Operation :
* : Z×Z → Z , a*b = a - b - 2
★ To find : 7*(-4) = ?
We have ;
a*b = a - b - 2
Thus ,
=> 7*(-4) = 7 - (-4) - 2
=> 7*(-4) = 7 + 4 - 2
=> 7*(-4) = 9
Hence , 7*(-4) = 9
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