Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:

Let R₁ and R₂ be two relation defined as follows :
R₁ = {(a, b) $$ \in $$ R² : a² + b² $$ \in $$ Q} and
R₂ = {(a, b) $$ \in $$ R² : a² + b² $$ \notin $$ Q},
where Q is the set of all rational numbers. Then :

Consider the two sets :
A = {m $$ \in $$ R : both the roots of
x² – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?