By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cap \)C) = (A\(\times\)B) \(\cap \) (A\(\times\)C)

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cup \)C) = (A\(\times\)B) \(\cup \) (A\(\times\)C)

Let A = {a, b, c}, and R = {(a, a) (b, b) (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it 
(i) reflexive
(ii) symmetric
(iii) transitive
(iv) equivalence

Prove that the relation "friendship" is not an equivalence relation on the set of all people in Chennai.

Let S = {1, 2, 3} and \(\rho\) = {(1, 1), (1, 2), (2, 2), (1, 3), (3, 1)}.
(i) Is \(\rho\) reflexive? If not, state the reason and write the minimum set of ordered pairs to be included to p so as to make it reflexive.
(ii) Is \(\rho\) symmetric? If not, state the reason, write minimum number of ordered pairs to be included to \(\rho\) so as to make it symmetric and write minimum number of ordered pairs to be deleted from p so as to make it symmetric,
(iii) Is \(\rho\) transitive? If not, state the reason, write minimum number of ordered pairs to be included to \(\rho\) so as to make it transitive and write minimum number of ordered pairs to be deleted from \(\rho\) so as to make it transitive.
(iv) Is \(\rho\) an equivalence relation? If not, write the minimum ordered pairs to be included to \(\rho\) so as to make it an equivalence relation.

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) not reflexive, not symmetric, not transitive.
(ii) not reflexive, not symmetric, transitive.

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) not reflexive, symmetric, not transitive.
(ii) not reflexive, symmetric, transitive. 

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) reflexive, not symmetric, not transitive.
(ii) reflexive, not symmetric, transitive.

Let A = {0,1, 2, 3}. Construct relations on A of the following types:
(i) reflexive, symmetric, not transitive.
(ii) reflexive, symmetric, transitive.