Question

If P={3,4,5} and Q={2,3,4}, then find P×Q and the set of the ordered pair in the following relation P top Q.

a) P×Q={(3,2),(3,3),(3,4),(4,2),(4,3),(4,4),(5,2),(5,3),(5,4)}
b) P×Q={(2,3),(3,4),(4,5)}
c) P×Q={(3,2),(4,3),(5,4)}
d) P×Q={(2,3),(3,4),(4,5),(5,2),(5,3),(5,4)}

Answer 1

The Cartesian product of sets P and Q is {(3,2),(3,3),(3,4),(4,2),(4,3),(4,4),(5,2),(5,3),(5,4)}. The set of ordered pairs in the relation P top Q cannot be determined without more information.

Step-by-step explanation:

To find the Cartesian product (P×Q) of two sets, you take each element of the first set (P) and pair it with every element of the second set (Q). So in this case, we have P={3,4,5} and Q={2,3,4}. Pairing each element of P with every element of Q gives us the set of ordered pairs: {(3,2),(3,3),(3,4),(4,2),(4,3),(4,4),(5,2),(5,3),(5,4)}. So option a) P×Q={(3,2),(3,3),(3,4),(4,2),(4,3),(4,4),(5,2),(5,3),(5,4)} is the correct answer.

The set of ordered pairs in the relation P top Q depends on the specific definition of the relation. Without more information, we cannot determine the set of ordered pairs in the relation. Therefore, none of the options provided (a), b), c), d)) can be determined as the correct answer.