Questions: Determine whether the statement below is true or false. (8,3)=(3,8) Is the statement true or false?

Solution Steps

To determine whether the statement \((8,3)=(3,8)\) is true or false, we need to understand that ordered pairs are equal if and only if their corresponding elements are equal. In this case, the first elements (8 and 3) and the second elements (3 and 8) are not equal, so the statement is false.

Ordered pairs \((a, b)\) and \((c, d)\) are equal if and only if \(a = c\) and \(b = d\). This means that both the first and second elements of the pairs must be identical for the pairs to be considered equal.

Given the ordered pairs \((8, 3)\) and \((3, 8)\), we compare their corresponding elements:

• First elements: \(8 \neq 3\)
• Second elements: \(3 \neq 8\)

Since neither the first nor the second elements are equal, the ordered pairs are not equal.

Final Answer