Question

If the longest chain in a partial order is of length l, then the partial order can be written as _____ disjoint antichains.

(a) l^2

(b) l+1

(c) l

(d) l^l

I had been asked this question by my school teacher while I was bunking the class.

The query is from Relations topic in section Relations of Discrete Mathematics

Answer 1

Right answer is (c) l

Explanation: If the length of the longest chain in a partial order is l, then the elements in the POSET can be partitioned into l disjoint antichains.