Let $L$ be the set of all straight lines in a plane and the relation $R$ on $L$ is defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is:

Let $R_1$ and $R_2$ be two relations on a set $A$. Choose the incorrect statement.

Let $A = \{-4, -3, -2, 0, 1, 3, 4\}$ and $R = \{(a, b) \in A \times A : b = |a| \text{ or } b^2 = a + 1\}$ be a relation on $A$. Then the minimum number of elements that must be added to the relation $R$ so that it becomes reflexive and symmetric is $........$.

Show that the relation $R$ defined in the set $A$ of all polygons as $R = \{(P_{1}, P_{2}) : P_{1} \text{ and } P_{2} \text{ have the same number of sides}\}$,is an equivalence relation. What is the set of all elements in $A$ related to the right-angled triangle $T$ with sides $3, 4, \text{ and } 5$?

Let $A = \{2, 3, 5, 7, 9\}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x \le 3y$. 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 symmetric relation. Then $l + m$ is equal to:

On set $A = \{1, 2, 3\}$, relations $R$ and $S$ are given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$ and $S = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$. Then,