GATE | GATE-CS-2016 (Set 2) | Question 38

Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:

I.  Each compound in U \\ S reacts with an odd number of compounds.
II.  At least one compound in U \\ S reacts with an odd number of compounds.
III.  Each compound in U \\ S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

(A)

Only I

(B)

Only II

(C)

Only III

(D)

None

Answer

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