canonical expression in compact form??

Question

Does canonical expression in compact form need to have all the variables in it?

For example, if I have a,b,c, and d variables and the compact form comes out to be just c+d, is this possible?

For example: If I have an expression

=(a'b'cd)+(a'bc'd')+(a'bcd)+(ab'cd)+(abc'd')+(abcd')

=a'+cd+abd'

=cd+bd'

=c+b

Am I doing it right?

Answer 1

It is possible. $(a \vee \neg a) \wedge b$ is equivalent to $b$, for instance.

However, your reduction is not correct. For example, in the last equality, let $b = 1, d = 1, c = 0$; then your third line is $0$ but the last line is $1$.