Question

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {( a , b ): b = a + 1} is reflexive, symmetric or transitive.

Answer 1

The given relation R in set A={1,2,3,4,5,6} is defined as R={( a,b ):b=a+1}.

Thus, R={ ( 1,2 ),( 2,3 ),( 3,4 ),( 4,5 ),( 5,6 ) }.

Since, ( 1,1 ),( 2,2 ),( 3,3 ).....( 6,6 )∉R, hence R is not reflexive.

Since, ( 1,2 )∈R but ( 2,1 )∉R. Hence, Ris not symmetric.

Since, ( 1,2 ),( 2,3 )∈R but ( 1,3 )∉R, hence Ris not transitive.

Therefore, the given relation R={( a,b ):b=a+1} in the set A={1,2,3,4,5,6} is not reflexive, symmetric, or transitive.