Is the number of min terms always equal to the number of max terms , for a boolean function?
This is one of the Most misunderstood concept by most of the students.
The definition of MinTerm is that "For a function on n variables, any product term of these variables in which every variable is present either in original form or in complemented form, is called MinTerm."
So WHATEVER function you take for 2 variables, there will ALWAYS be 4 MinTerms, similarly 4 maxterms.
NOTE that in the definition of MinTerm, we Don't have the requirement that the function output for a minterm must be 1.
Any function can be written as summation(OR) of SOME of its MinTerms (Summation of those MinTerms for which function output is 1.)
For ANY function on variables a,b we have the following MinTerms :
It does not matter what function you have over these two variables.
MinTerms for which function output is 1 are called 1-minTerms by some authors.
MinTerms for which function output is 0 are called 0-minTerms by some authors.
So a function can be written as OR of its 1-MinTerms.
How many minterms are there for the function "a+b" over boolean variables a,b ?
Answer will be 4, NOT 3.
How many maxterms are there for the function "a+b" over boolean variables a,b ?
Answer will be 4, NOT 1.
Can we say that for a boolean function to be self dual, should satisfy the above condition as well as no mutual exclusive terms should be present?
EVERY function has same number of MinTerms and MaxTerms.
A function is Self Dual if and only if the number of 1-Minterms and number of 0-minterms is same AND Function should not contain two mutually exclusive terms.