1. Unless rock sample X comes from Venus, then it does not contain silicon. Rock sample X came either from Mars or Venus. Research shows that rock sample X contains silicon. So,
rock sample X came from Mars.
2. It is impossible for people to achieve happiness without a lot of money. And people must
work hard in order to earn a lot of money. Mary has a lot of money. Therefore, Mary
worked hard.
Sample
All students who graduate from universities must be able to write good academic papers. A
student must have an adequate command of English in order to write good academic papers,
Unless you study English hard, you definitely cannot achieve an adequate command of English.
Therefore, those who graduate from universities must have studied English hard.
Marking scheme:
1. Correct answer about "valid" or "invalid" (1%)
2. Correct identification of pattern (1.5%)

1. Valid
2. Pattern:
P: graduate from universities
Q: write good academic papers
R: adequate command of English
S: study English hard
a. (If P then Q)
b. (If Q then R)
c. (If not S then not R; or if R then S)
d. Therefore, (If P then S)
Explanation: This argument has a pattern of hypothetical syllogism (if P then Q, if Q then Rand
If R then S, therefore, If P then S).​