176k views
1 vote
Solve by intersection graph: Let S be a set of Moumineen with six elements, and R:=Love be a relation on S such that for s,t ∈ S, sRt if s loves t. Construct a graph G for (S , R) that has a vertex for each element of S and has an edge connecting the two vertices representing the two elements if these elements are R-related. Hence find the number of edges in G for (S , R) if S has n elements.

(a) The graph G has n vertices.
(b) Each element of S is connected to every other element in G.
(c) The graph G is a complete graph.
(d) The number of edges in G is equal to n(n-1)/2.

User Estebanrv
by
7.8k points

1 Answer

2 votes

Final answer:

To solve by intersection graph, construct a graph with n vertices representing elements in S and connect them if they are R-related (love each other). This yields a complete graph with n(n-1)/2 edges, since each element connects to every other unique element without repeating connections.

Step-by-step explanation:

To solve by intersection graph for a set S with n elements, where a relation R exists such that for any two elements s and t in S, sRt if s loves t, we construct a graph G. In this graph, each vertex represents an element of S, and an edge connects two vertices if there is a love relationship (R-related) between them. For n elements in S:

Since every element is connected to every other element, for a set S with n elements, there are n(n-1)/2 edges because each connection is counted only once.

User SmasherHell
by
7.6k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.