MCQ_SINGLE

If $A = {x \in R : |x| < 2}$ and $B = {x \in R : |x – 2| \geq 3}$; then :

NUMERICAL

Let $A=\{1,2,3,4\}$ and $\mathrm{R}$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $\mathrm{R}$ is ____________.

MCQ_SINGLE

Let $R_1 = \{(a, b) \in N \times N : |a - b| \le 13\}$ and $R_2 = \{(a, b) \in N \times N : |a - b| \ne 13\}$. Then on N :

NUMERICAL

The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is __________.

MCQ_SINGLE

Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R = {(x, y) ∈ W × W |$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is

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