NUMERICAL

Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$. Then the number of elements in the set $\{C \subseteq A: C \cap B \neq \phi\}$ is ___________.

MCQ_SINGLE

For $\alpha \in N$, consider a relation $R$ on $N$ given by $R = \{(x, y) : 3x + \alpha y$ is a multiple of $7\}$. The relation $R$ is an equivalence relation if and only if :

MCQ_SINGLE

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation $R$ 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

MCQ_SINGLE

Let $R = {(P, Q) | P$ and $Q$ are at the same distance from the origin} be a relation, then the equivalence class of $(1, −1)$ is the set :

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