Consider the following relation on set B = {1, b, {1}, {b}, {1, b}}:

P = {(1, b), (b, {1, b}), ({1, b}, 1), ({b}, 1), (1, {1})}.

The relation P does not satisfy trichotomy. Which alternative contains the correct ordered pairs that should be added to P in order to satisfy trichotomy?

Select one:

a.

({1}, b), (b, {b}), ({b}, {1, b}) & ({1, b}, {1})

b.

(b, {1}), (b, {b}), ({1}, {b}) & ({1, b}, {1, b})

c.

(b, {1}), (b, {b}), (b, 1), ({1}, {1, b}) & ({1, b}, {b})

d.

(b, {1}), ({b}, b), ({1}, {b}), ({b}, {1, b}) & ({1, b}, {1})