Browse Questions

# 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}

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

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.