Q. Over the set A={1,2,3,4,5} two partitions a and b are defined as a={{1,2,3},{4},{5}} and b={{1},{2,3},{4,5}}.The MEET and JOIN(under refinement relations between partitions ) are respectively.

A) {(1),(2,3),(4),(5)} and {(1,2,3),(4,5)}

B){(1,2,3)(4,5)} and{(1,2),(3),(4,5)}

C){(1,2),(3,4)(5)} and {(1,2),(3,4),(5)}

D){(1,2,3,4,5)} and {(1),(2),(3),(4),(5)}

Suppose , we have two partition of set S

P1 ={A1,A2,A3....} and P2 = {B1,B2,B3.....}

We can say that "P1 is refinement of P2 if every Ai is a subset of some Bj"

According to given question

option (a) satisfy refinement property.

why not option D