Let $${R_1}$$ and $${R_2}$$ be two equivalence relations on a set. Consider the following assertions:

(i)$$\,\,\,\,{R_1} \cup {R_2}$$ is an euivalence relation
(ii)$$\,\,\,\,{R_1} \cap {R_2}$$ is an equivalence relation

Which of the following is correct?

Suppose $$A$$ is a finite set with $$n$$ elements. The number of elements in the Largest equivalence relation of $$A$$ is

Consider the following set a equations
x + 2y = 5
4x + 8y = 12
3x + 6y + 3z = 15 This set

In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 persons speak both Kannada and English. How many people speak all three languages?