JEE Advanced 2024 · Paper 2, Mathematics question 14

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Let $S = \{1, 2, 3, 4, 5, 6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties:

1. $R$ has exactly 6 elements.
2. For each $(a, b) \in R$, we have $|a - b| \ge 2$.

Let $Y = \{R \in X : \text{The range of } R \text{ has exactly one element}\}$ and $Z = \{R \in X : R \text{ is a function from } S \text{ to } S\}$.

Let $n(A)$ denote the number of elements in a set $A$.