Final answer:
The Cartesian product of P and Q is {(1, 4), (1, 6), (2, 4), (2, 6)}. The relation R such that x + y is greater than or equal to 4 is R = {(1, 4), (1, 6), (2, 4), (2, 6)}.
Step-by-step explanation:
The Cartesian product of two sets P and Q, denoted P x Q, is the set of all possible ordered pairs where the first element comes from set P and the second element comes from set Q. In this case, P = {1, 2} and Q = {4, 6}. Therefore, P x Q = {(1, 4), (1, 6), (2, 4), (2, 6)}.
To find a relation such that x + y is greater than or equal to 4, we can consider the set of all ordered pairs where the sum of the two elements is greater than or equal to 4.
One possible relation is R = {(1, 4), (1, 6), (2, 4), (2, 6)}. This relation contains all the ordered pairs from P x Q where the sum of the elements is greater than or equal to 4.