Let R be a relation in the set N given by R={(a,b): a+b=5, b>1}. Which of the following will satisfy the given relation?

The correct option is (2,3) ∈ R.

Let us break down the relation step-by-step to understand why this option satisfies it.
The relation $R$ is defined on the set of natural numbers $N$ as:
$$R=\{(a,b):a+b=5,b>1\}$$
Here, both $a$ and $b$ must be natural numbers ($a,b\in N$ where $N=\{1,2,3,...\}$).

To satisfy the relation, an ordered pair $(a,b)$ must satisfy two conditions simultaneously:
1. Condition 1: $a+b=5$
2. Condition 2: $b>1$

Let us test the given option $(2,3)$:
Here, $a=2$ and $b=3$.
First, we check Condition 2: $b=3$, and since $3>1$, this condition is satisfied.
Next, we check Condition 1:
$$a+b=2+3=5$$
Since $2+3=5$, Condition 1 is also satisfied.
Since both conditions are met and both 2 and 3 are natural numbers, the ordered pair $(2,3)$ belongs to the relation $R$.