Question

Solve by intersection graph: Let ( S ) be a set of 'Moumineen' with six elements and ( R = Love ) be a relation on ( S ). Construct a graph ( G ) for ( (S, R) ) with edges connecting R-related elements. Find the number of edges in ( G ) if ( S ) has ( n ) elements.

a) 6
b) 15
c) 18
d) 21

Answer 1

To solve this problem, we need to construct a graph based on a relation and find the number of edges in the graph.

Step-by-step explanation:

The graph for the relation (R = Love) on the set (S) with six elements can be constructed by connecting the elements that are related by the relation. In this case, the relation (R) connects the elements of (S) based on love. So, if two elements in (S) love each other, we draw an edge between them in the graph (G).

Since there are six elements in (S), and we need to find the number of edges in the graph (G), we need to determine the number of pairs of elements that are love-related. This can be done using the combination formula C(n, 2), where n is the number of elements in (S). In this case, n = 6.

Using the combination formula, we find that C(6, 2) = 6! / ((6-2)! * 2!) = 6 * 5 / 2 * 1 = 15. So, the number of edges in the graph (G) is 15.