Which of the following relations has this characteristic:
The relation is a function containing two ordered pairs. Reversing the components in each ordered pair results in a relation that is not a function.
A) {(0, 2), (0, 3)}
B) {(2, 3), (3, 2)}
C) {(3, 1), (4, 1)}
D) {(4, 5), (2, 3)}
To determine which of the given relations has the specified characteristic, we need to reverse the components in each ordered pair and check if the resulting relation is a function.
Let's go through each option:
A) {(0, 2), (0, 3)}
If we reverse the components in each ordered pair, we get {(2, 0), (3, 0)}. In this case, both pairs share the same second component (0), so the reversed relation is not a function.
B) {(2, 3), (3, 2)}
If we reverse the components in each ordered pair, we get {(3, 2), (2, 3)}. In this case, both pairs have different second components (2 and 3) which are distinct, so the reversed relation is a function.
C) {(3, 1), (4, 1)}
If we reverse the components in each ordered pair, we get {(1, 3), (1, 4)}. In this case, both pairs share the same second component (1), so the reversed relation is not a function.
D) {(4, 5), (2, 3)}
If we reverse the components in each ordered pair, we get {(5, 4), (3, 2)}. In this case, both pairs have different second components (4 and 2) which are distinct, so the reversed relation is a function.
Therefore, the answer is option D) {(4, 5), (2, 3)}.
To find the relation that has the characteristic mentioned, we need to reverse the components in each ordered pair and check if the resulting relation is a function. Let's go through each option:
A) {(0, 2), (0, 3)} - If we reverse the components, we get {(2, 0), (3, 0)}. From this, we can see that the x-coordinate (the first component) of both ordered pairs is the same, which violates the definition of a function. Therefore, option A is not the correct answer.
B) {(2, 3), (3, 2)} - If we reverse the components, we get {(3, 2), (2, 3)}. In this case, the x-coordinate (the first component) of both ordered pairs is different, so it satisfies the definition of a function. Therefore, option B is not the correct answer.
C) {(3, 1), (4, 1)} - If we reverse the components, we get {(1, 3), (1, 4)}. In this case, the x-coordinate (the first component) of both ordered pairs is the same, which violates the definition of a function. Therefore, option C is not the correct answer.
D) {(4, 5), (2, 3)} - If we reverse the components, we get {(5, 4), (3, 2)}. In this case, the x-coordinate (the first component) of both ordered pairs is different, so it satisfies the definition of a function. Therefore, option D is the correct answer.
Therefore, the relation that has the characteristic mentioned is option D) {(4, 5), (2, 3)}.