P `o+` Q means P is greater than Q.
P `underlinecancel("©")` Q means P is either greater than or equal to Q.
P = Q means P is equal to Q.
P @ Q means P is smaller than Q.
P `underlinecancel("@")` Q means P is either smaller than equal to Q.
Statements: Q @ R, C `o+` D, F `underlinecancel("©")` R, D = F
Conclusions: I. Q @ C II. C `o+` F

Options

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

Answer

D

Explanation

Statements: `Q lt R, C gt D, F ge R, D = F`
Conclusions: I. `Q lt C` II. `C gt F`
F or I, all elements are relevant and need to be used, combine `Q lt R` with `F ge R` to get `Q lt R le F` to given `Q lt F`. So, we eliminate R and get a conclusion between Q and F. Now, let us put D = F in `Q lt F` to get `Q lt D`. So, we eliminate F this time and get a conclusion between Q and D. Now, `Q lt D` and `C gt D` give `Q lt D lt C` to give `Q lt C`. So, I follows. II follows from `C gt D` and D = F.