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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let \(\ast '\) be the binary operation on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \ast ' b = H.C.F\,. of\, a \,and \,b.\) Is the operation same as the operation \(\ast\) defined in the table below? \begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}

$\begin{array}{1 1} \text{Yes, the two operations are the same} \\ \text{No, they are different} \end{array} $

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Toolbox:
  • To compare two binary operations we write the corresponding operation table and compare each entry in the table.
  • The highest common factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
The binary operation ,$*'$ on the set $\{1,2,3,4,5\}$ defined by $a*'b= $ HCF$(a,b)$
The highest common factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
We can observe from the table that $a \ast' b =1$ and $ a \ast' a = a$, which is nothing but the HCF$(a,b)$.
Therefore the two operations are the same.
answered Mar 20, 2013 by balaji.thirumalai
 

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