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In this paper we have introduce two new concepts namely edge stable sets& edge independent sets in hypergraphs. We have proved a necessary and sufficient condition under which an edge stable set is a maximal edge stable set. We have also proved an important result that an edge stable set of a hypergraph is a maximal edge stable set of it if and only if it is a minimal edge h-dominating set of that hypergraph. A characterization of edge independent set is also given by us and some results related to edge independent set in hypergraphs have been proved.

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In this paper we have introduced maximum edge independent sets in hypergraphs where a maximum edge independent set is an edge independent set with maximum cardinality. We have proved that the edge independence number of a hypergraph (with minimum edge degree at least two) remain same or decreases when an edge is removed from the hypergraph. In particular we have proved that the edge independence number of a hypergraph (with minimum edge degree at least two and edge independence number is greater than one) decreases if and only if there is a maximum edge independent set which contains the edge. We have also considered the edge independence numbers of the subhypergraph and the partial subhypergraph obtained by removing a vertex from the hypergraph. We observe that edge independence number of the finite projective plane always increases when any vertex is removed from the hypergraph and the subhypergraph is considered and the edge independence number remains same when any vertex is removed and the partial subhypergraph is considered.

In this paper we further prove more results about edge domination in hypergraphs. In particular we prove necessary & sufficient conditions under which the edge domination number of a hypergraph increases or decreases when a vertex is removed from the hypergraph. We have proved that a subset F of E (G) is an edge dominating set of G iff it is a dominating set in G* (Where G* is dual hypergraph of G) also we have proved that if E (G-v) > E (G) & if F is a minimum edge dominating set of G then there is an edge e containing v  e  F & Prn [e, F] contains two distinct edges.