Question

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.

Answer 1

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.