Question

Let r be the following relation on the set Z, the set of integers

xry if and only if x = y²
Which of the following are elements of r? Select all that apply.
A. (64, 8)
B. (4,3)
C. (25,-5)
D. (5, 25)

Answer 1

The relation r on the set Z, the set of integers, is defined as xry if and only if x = y². The elements of r are determined by checking if the given pairs satisfy this condition. Only (5, 25) satisfies the condition.

Step-by-step explanation:

The relation r on the set Z, the set of integers, is defined as xry if and only if x = y². To determine which elements are in r, we need to check if the given pairs satisfy the condition. Let's go through each option:

• A. (64, 8): 8 is not equal to 64², so (64, 8) is not an element of r.
• B. (4,3): 3 is not equal to 4², so (4, 3) is not an element of r.
• C. (25,-5): -5 is not equal to 25², so (25, -5) is not an element of r.
• D. (5, 25): 25 is equal to 5², so (5, 25) is an element of r.

Therefore, the pairs that are elements of r are (5, 25).