Question

Consider the binary opeartion $\stackrel{\Lambda }{}$ on the set {1,2,3,4,5} defined by a $\stackrel{\Lambda }{}$ b =min {a,b}. Write the multiplication table of the operation.

Answer 1

The binary operation ^ on the set {1,2,3,4,5} is defined as a $\stackrel{\Lambda }{}$ b =min {a,b} for $a,b\in \{1,2,3,4,5\}$.
Thus, the operation table for the given operation $\stackrel{\Lambda }{}$ can be given as

$\begin{array}{cccccc}\stackrel{\Lambda }{}& 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 2& 2& 2\\ 3& 1& 2& 3& 3& 3\\ 4& 1& 2& 3& 4& 4\\ 5& 1& 2& 3& 4& 5\end{array}$