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

Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _________.

MCQ_SINGLE

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor transitive

MCQ_SINGLE

Consider the two sets: A = {$m ∈ R$: both the roots of $x^2 – (m + 1)x + m + 4 = 0$ are real} and B = [–$3$, $5$). Which of the following is not true?

NUMERICAL

4 Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _________.

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