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

This question has appeared in model paper 2012

Toolbox:
• When number of elements in a set A is small, we can express a binary operation ∗ on the set A through a table called the operation table for the operation ∗.
• Given a binary operation * on a set $A: A \times A \to A$. If $A=\{a_1,a_2......a_n\}$ Then operating table will have n rows and n columns with $(i,j)^{th}$ entry being $a_i*a_j$
Binary operation $\wedge$ on set $\{1,2,3,4,5\}$ is defined by $a \wedge b = min \{a, b\}, \; a,b \in \{1,2,3,4,5\}$
Consider $a=1, b=1$, we see that minimum of 1 and 1 is 1, so $a \wedge b = 1 \wedge 1=1$
Similarly $1 \wedge 2 = 1$,$\; 1 \wedge 3 = 1$ and so on...
Therefore we can construct the following operation table:

^ 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

edited Mar 19, 2013