How many valuations of these literals satisfy this expression? considering all the possible valuations of literals A, B, C, D, E, F, G and H (256 valuations in total), how would you go about finding how many of these valuations satisfy this expression:
$$ (A\rightarrow B) \wedge (B\rightarrow C) \wedge (D\rightarrow E) \wedge (F\rightarrow G) \wedge (G\rightarrow H)$$
I know I could draw the truth table with all the possible valuations, but what's a more efficient method? The solution that I calculated through software simulation should be 48.

Note that you can divide the expression in three parts:
$$
\underbrace{(A\rightarrow B) \wedge (B\rightarrow C)}_{P} \wedge \underbrace{(D\rightarrow E)}_{Q} \wedge \underbrace{(F\rightarrow G) \wedge (G\rightarrow H)}_{R}
$$
The value of $P$ depends only on $A,B,C$, the value of $Q$ depends only on $D,E$, and the value of $R$ depends only on $F,G,H$. So if $N_P$ is the number of choices of $A,B,C$ for which $P$ is true, $N_Q$ is the number of choices of $D,E$ for which $Q$ is true, and $N_R$ is the number of choices of $F,G,H$ for which $R$ is true, the total number is 
$$
N_P N_Q N_R.
$$
