Check whether the relation `R` defined on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6}` as `R={(a ,\ b): b=a+1}` is reflexive, symmetric or transitive.

Explanation

To determine whether the relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5, 6\} \) as \( R = \{(a, b) : b = a + 1\} \) is reflexive, symmetric, or transitive, we will analyze each property step by step.

### Step 1: Check if the relation is Reflexive
A relation is reflexive if for every element \( a \in A \), the pair \( (a, a) \) is in \( R \).

- For \( a = 1 \), \( (1, 1) \) is not in \( R \) because \( 1 \neq 1 + 1 \).
- For \( a = 2 \), \( (2, 2) \) is not in \( R \) because \( 2 \neq 2 + 1 \).
- For \( a = 3 \), \( (3, 3) \) is not in \( R \) because \( 3 \neq 3 + 1 \).
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