P `alpha` Q means P is greater than Q.
P `beta` Q means P is either greater than or equal to Q.
P `gamma` Q means P is equal to Q.
P `delta` Q means P is smaller than Q.
P `eta` Q means P is either smaller than or equal to Q.
Statements: L `beta`M, O `gamma`N, L `delta`H, M `gamma` O
Conclusions: I. L `gamma`N II. L `alpha`N

Options

A. if only conclusion I is true,
B. if only conclusion II is true,
C. if either I or II is true,
D. if both I and II are true.

Answer

D

Explanation

Given Statements: `L beta M, O gamma N, L delta H, M gamma O`
(i) Conclusion I: `L gamma N`
It has two terms L and N. Here, we see that L and N do not appear with a common term in any pair of statements. This means that in this case more than two statements may be relevant for us. Here, we see that N appears only once (with O) in `O gamma N.` Now, O appears with M (in M `gamma` O) and M appears with L (in L `beta` M). Hence, in this case we have:
`O gamma N, M gamma O, L beta M`
as our relevant statements.
(ii) Conclusion II: `L alpha N`.
Relevant statements are `O gamma N, M gamma O, L beta M`.
(For explanation see explanation for conclusion I).