The minimum number of elements that must be added to the relation R = ( a , b ) , ( b , c ) on the set a , b , c so that it becomes symmetric and transitive is:

Step-by-step solution

Given: A = a , b , c , d And, R = a , b , b , c For symmetric relation, we must add b , a ,   c , b . So, R = a , b , b , a ,   b , c , c , b . For transitive relation, we must add a , c ,   b , b ,   c , a ,   a , a ,   c , c Hence, R = b , a ,   c , b ,   a , c ,   b , b ,   c , a ,   a , a ,   c , c ,   a , b ,   b , c So, number of new elements added = 7