MCQ_SINGLE

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$. Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ is :

MCQ_SINGLE

Let R be a relation from the set ${1, 2, 3, …, 60}$ to itself such that $R = {(a, b) : b = pq}$, where $p, q \geqslant 3$ are prime numbers}. Then, the number of elements in R is :

MCQ_SINGLE

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$. Then the distance of the point $P(m,n)$ from the point $Q(-2,-3)$ is :

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 a relation on $Z \times Z$ defined by $(a, b)R(c, d)$ if and only if $ad - bc$ is divisible by $5$. Then $R$ is

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