Question

Let R = {(2, 6), (1, 8), (2, 4), (1, 4), (1, 6)}. If R is a relation defined on a set A, what is the smallest possible set A?

• A. {4, 6, 8}
• B. 16
• C. {1, 2, 4, 6, 8}

Answer 1

Answer: (C)

{1, 2, 4, 6, 8}

Answer 2

For a relation R to be defined on a set A, it must be a subset of A x A. This implies that every element appearing in any ordered pair of R must belong to A. The set A must contain all the first elements (domain elements) and all the second elements (range elements) of the ordered pairs in R. Given relation R = {(2, 6), (1, 8), (2, 4), (1, 4), (1, 6)}. The set of first elements is {2, 1}. The set of second elements is {6, 8, 4}. The smallest possible set A must include all these elements. Therefore, A is the union of these two sets: $A = \{1, 2\} \cup \{4, 6, 8\} = \{1, 2, 4, 6, 8\}$.