Logic and sets · Binary operations · Operation tables · Associativity · Case analysis
Problem 1, 2016
← Prev · 3 / 3 · Next →An operation \(\diamond\) on the set \(G = \{1, 2, 3, \dots, 2016\}\) is given by the table
\[ \begin{array}{c|cccccc} \diamond & 1 & 2 & 3 & 4 & \cdots & 2016 \\ \hline 1 & 5 & 5 & 5 & 5 & \cdots & 5 \\ 2 & 1 & 2 & 5 & 5 & \cdots & 5 \\ 3 & 4 & 3 & 5 & 5 & \cdots & 5 \\ 4 & 5 & 5 & 5 & 5 & \cdots & 5 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ 2016 & 5 & 5 & 5 & 5 & \cdots & 5 \end{array} \]
where the row gives the left operand and the column the right one, and every entry of the table that is not displayed explicitly equals \(5\). Decide whether \(\diamond\) is associative.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2016, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source