Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $3\}$ is given by

The relation "is subset of" on the power set $P(A)$ of a set $A$ is

Let $P = \{ (x, y) | x^2 + y^2 = 1, x, y \in \mathbb{R} \}$. Then $P$ is:

Let $X = R \times R$. Define a relation $R$ on $X$ as: $(a_1, b_1) R (a_2, b_2) \Leftrightarrow b_1 = b_2$. Statement-$I$: $R$ is an equivalence relation. Statement-$II$: For some $(a, b) \in X$,the set $S = \{(x, y) \in X : (x, y) R (a, b)\}$ represents a line parallel to $y = x$. In the light of the above statements,choose the correct answer from the options given below:

Let $R$ and $S$ be two non-void relations on a set $A$. Which of the following statements is false?