I am currently studying the textbook Digital Design by Mano, and learned that the Boolean function can be expressed algebraically from a given truth table by forming a minterm for each combination of the variables that produces a 1 in the function and then taking the OR of all those terms.
If the following truth table was given,
x y|F minterms
----- ---------------
0 0|0 m_0 | x'y'
0 1|1 m_1 | x'y
1 0|0 m_2 | x y'
1 1|0 m_3 | x y
then the boolean function can be expressed as $$ F=m_1+m_3=x'y+xy. $$
So far the boolean function can be equal to either 1 or 0. What if there are characters in the function value, not 0 and 1?
x y|F*
-----
0 0|a
0 1|b
1 0|c
1 1|d
My initial guess for the boolean function $F^*$ was $$ F^*=m_0\cdot a + m_1\cdot b + m_2\cdot c + m_3\cdot d, $$ but I can't find any reference to support my assumption. Is my initial guess correct? And where do I find supporting references?