Q.Write the truth table for 3 variable input with min term designations.

For three variables A, B, C there are $2^3 = 8$ input combinations, and each row is labelled with its minterm designation $m_0$ to $m_7$ taken as the decimal value of A B C. …

[!TLDR]

Three variables give 8 rows, labelled $m_0$ to $m_7$ by the decimal value of A B C; a variable is complemented in a minterm wherever its bit is 0.

With three input variables A, B and C there are $2^3 = 8$ possible combinations, listed in the truth table from 000 to 111. Each row is given a minterm designation $m_i$, where the subscript $i$ is the decimal equivalent of the binary input pattern (A being the most significant bit). In writing the minterm expression for a row, each variable is complemented if its value in that row is 0 and left uncomplemented if it is 1. …