MCQ_SINGLE

Let $R = \{(1, 2), (2, 3), (3, 3)\}$ be a relation defined on the set $\{1, 2, 3, 4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, is:

NUMERICAL

Let A = {n $\in$ N | n2 $\le$ n + 10,000}, B = {3k + 1 | k$\in$ N} an dC = {2k | k$\in$N}, then the sum of all the elements of the set A $\cap$(B $-$ C) is equal to _____________.

NUMERICAL

The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is __________.

MCQ_SINGLE

Let $R$ be the set of real numbers. Statement I: $A = \{(x, y) \in R \times R: y - x \text{ is an integer }\}$ is an equivalence relation on $R$. Statement II: $B = \{(x,y) \in R \times R: x = \alpha y \text{ for some rational number } \alpha\}$ is an equivalence relation on $R$.

NUMERICAL

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.

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