Question

A king has unflinching loyalty from eight of his ministers $M_1$ to $M_8$, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three person selected.
$M_1$ likes fishing and smoking, but hates gambling,
$M_2$ likes smoking and drinking, but hates fishing,
$M_3$ likes gambling, but hates smoking,
$M_4$ likes mountaineering, but hates drinking,
$M_5$ likes drinking, but hates smoking and mountaineering,
$M_6$ likes fishing, but hates smoking and mountaineering,
$M_7$ likes gambling and mountaineering, but hates fishing, and
$M_8$ likes smoking and gambling, but hates mountaineering.
Who are the four people selected by the king?

• A. M₁, M₂, M₅, M₆
• B. M₃, M₄, M₅, M₆
• C. M₄, M₅, M₆, M₈
• D. M₁, M₂, M₄, M₇

Answer 1

The correct option is D

M₁, M₂, M₄, M₇

Answer option (a) is rejected because$M_1$ hates Gambling which is not hated by any of the other three. Answer option (b) is rejected because $M_3$ likes Gambling which is not liked by any of the other three. Answer option (c) is rejected because$M_4$ likes Mountaineering which is not liked by any of the other three. Option (d) is the correct answer choice because it fulfills both the conditions