Which one of the above statements is ALWAYS TRUE?

Consider a set of U

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:

  1. Each compound in U \ S reacts with an odd number of compounds.
  2. At least one compound in U \ S reacts with an odd number of compounds.
  3. Each compound in U \ S reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

  1. Only I
  2. Only II
  3. Only III
  4. None.

 

1Comment
Sumit Verma @sumitkgp
22 Jul 2017 11:18 pm

See the wonderful explanation of Ranita ma'am
http://www.techtud.com/doubt/algebra-set-theory-gate-2016-set-2