# Recent questions tagged p25

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### Let $$\ast$$ be the binary operation on $$N$$ given by $$a\ast b=L.C.M\,.of\,a\,and\,b$$. Find \$\begin{array}{1 1}(i)\;\; 5 \ast7,\; 20 \ast 16 & (ii)\;\; Is\; \ast \;commutative?\$$iii)\;\; Is\; \ast \;associative? & (iv)\;\; Find\, the\,identity \, of \ast \, in N\\(v)\;\; Which \, elements\, of \, N\, are\, invertible\, for\, the\, operaation\,\ast ? & \;\end{array} ### 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}

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