MCQ_SINGLE

Consider the following relations $R = \{(x, y) | x, y$ are real numbers and $x = wy$ for some rational number $w\}$; $S = \{(\frac{m}{n}, \frac{p}{q}) | m, n, p$ and $q$ are integers such that $n, q \neq 0$ and $qm = pn\}$. Then

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 _________.

MCQ_SINGLE

Let $A = { (\alpha, \beta ) \in R \times R : |\alpha - 1| \leq 4$ and $|\beta - 5| \leq 6 }$ and $B = { (\alpha, \beta ) \in R \times R : 16(\alpha - 2)^{2}+ 9(\beta - 6)^{2} \leq 144 }$. Then

MCQ_SINGLE

The relation $R = \{(a, b) : gcd(a, b) = 1, 2a \neq b, a, b \in Z\}$ is:

NUMERICAL

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________

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