Let A = {1,2,3} and B = {2,3,4}, then which of the following relations is a function from A to B?

• A) { (1,2),(2,3),(3,4),(2,2)}
• B) { (1,2),(2,3),(1,3)}
• C) { (1,3),(2,3),(3,3)}
• D) { (1,1),(2,3),(3,4)}

To determine which of the given relations is a function from set A to set B, we need to check if each element in set A is associated with exactly one element in set B. Set A = {1, 2, 3} and set B = {2, 3, 4}.

Analyzing Each Option

Option A: { (1,2), (2,3), (3,4), (2,2) }

This relation includes the pair (2,2) which means the element 2 from A is related to two different elements (3 and 2) in B. Therefore, this is not a function.

Option B: { (1,2), (2,3), (1,3) }

Here, the element 1 from A is related to two different elements (2 and 3) in B. Thus, this relation is also not a function.

Option C: { (1,3), (2,3), (3,3) }

In this case, each element from A (1, 2, and 3) is related to exactly one element in B (3). Hence, this relation is a function.

Option D: { (1,1), (2,3), (3,4) }

The pair (1,1) indicates that 1 from A is related to 1, which is not in B. Therefore, this relation is not a function.

Final Answer

The only relation that qualifies as a function from A to B is Option C: { (1,3), (2,3), (3,3) }.