Let,
H = I leave my home early.
T = I get stuck in traffic.
C = I will be late to my class.
P = I will get scolded by my teacher.
A = I have gotten my attendance for the day.
Based on the given statements we can construct the Premises and Conclusion as follows:
P1: (~H or T) → (C and P).
P2: C → ~A
P3: A
C1: H
Now Premises are always true so:
- P3: A is true implies A = true,
- Using this in P2 we get C → ~(true) => C → false, Now in order for this Premise to be true C has to false or otherwise if C is true => True → false = false. Therefore so far we got A = true and C = false.
- Using the above info in P1 we get (~H or T) → ( false and P). This has to evaluate to True, Now RHS of implication will be false which leads to (~H or T) → false. So (~H or T) cannot be true as the Premise would compute to false, so (~H or T) = false. This is possible only when both ~H and T are false, so we get T = false and ~H = false => H = true which is the conclusion C1.
Therefore we can say that the conclusion is a valid one based on the given premises.