Deriving truth table from English description

Question

I'm trying to check if my truth table is correct since it largely depends on further parts of a larger problem.

Here is the English description:

The controller will turn on the headlights under the following conditions:

$$\begin{array}{l}\text{The manual switch is on (ManualSwitch = ’1′)}\\ \text{or} \\ \text{The car is running (CarOn = ’1′) and:} \\ \quad\text{it is raining (Raining = ’1′),}\\ \quad\text{it is night time (Daytime = ’0′),}\\ \quad\text{or both.}\\ \text{or both.} \end{array}$$ I'm representing it so that ManualSwitch = M, CarOn = C, Raining = R, Daytime = D, and HeadlightsOn = H. And X = Don't Care.

M     C     R     D     H
0     0     X     X     0
0     1     0     0     1
0     1     0     1     0
0     1     1     0     1
0     1     1     1     1
1     0     0     0     1
1     0     0     1     1
1     0     1     0     1
1     0     1     1     1
1     1     0     0     1
1     1     0     1     1
1     1     1     0     1
1     1     1     1     1

Answer 1

Note that by directly translating the English description to Boolean algebra, we obtain: $$ H = M + C(R + D') $$

Also, you should be able to condense the truth table to:

M     C     R     D     H
0     0     X     X     0
0     1     0     0     1
0     1     0     1     0
0     1     1     X     1
1     X     X     X     1