NUMERICAL

The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is _________.

MCQ_SINGLE

The relation $R = {(x, y) : x, y ∈ Z$ and $x + y$ is even $}$ is:

MCQ_SINGLE

Let $A = {-3, -2, -1, 0, 1, 2, 3}$. Let R be a relation on A defined by $xRy$ if and only if $0 \le x^2 + 2y \le 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l + m$ is equal to

MCQ_SINGLE

Among the relations $S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$ and $T = {(a, b) : a, b \in R, a^2 - b^2 \in Z}$,

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 __________.

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