Assertion (A): R, S, D and E are mid-points of OC, OB, AB and AC respectively, then DERS is a parallelogram.

Reason (R): DS ∥ AO ∥ ER and DS = ER = $\dfrac{1}{2}AO$.

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.

By mid-point theorem,

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

In △ABO,

D and S are respective midpoints of AB and BO.

∴ DS || AO and DS = $\dfrac{1}{2}$ AO [By mid-point theorem]……………..(1)

In △ACO,

E and R are respective midpoints of AC and CO.

∴ ER || AO and ER = $\dfrac{1}{2}$ AO [By mid-point theorem]………………(2)

From (1) and (2) we get,

DS || ER and DS = ER = $\dfrac{1}{2}$ AO

So, reason (R) is true.

We know that,

If one pair of opposite sides of a quadrilateral are equal in length and parallel, then the quadrilateral is a parallelogram.

∴ DERS is a parallelogram.

So, assertion (A) is true.

∴ Both A and R are true, and R is the correct reason for A.

Hence, option 3 is the correct option.