Which of the following relations are functions ?
F= {(1,2) (2,3) (3,5) (4,7)}
G= {(1,3) (1,4) (2,5) (2,6) (3,7)}
H= {(1,3) (2,6) (3,9), ..., (n, 3n), ... }
Thanks you!
F= {(1,2) (2,3) (3,5) (4,7)}
and
H= {(1,3) (2,6) (3,9), ..., (n, 3n), ...}
Which of the following relations is not a function?
a
F. {(3, 5), (7, 9), (4, 5), (2, 8)}
b
G. {(0, 1), (2, 5), (3, 6), (2, 7)}
c
H. {(1, 4), (0, 6), (4, 8), (3, 5)}
d
J. {(6, 8), (2, 3), (5, 7), (1, 9)}
To determine which of the given relations are functions, we need to analyze each relation and check if there are any repetitions in the first element (input) of each pair.
Let's analyze each relation one by one:
F = {(1,2) (2,3) (3,5) (4,7)}
In relation F, there are no repetitions in the first element (input) of each pair. Each input is unique. Therefore, F is a function.
G = {(1,3) (1,4) (2,5) (2,6) (3,7)}
In relation G, we can see that the first element (input) has repetitions. Both 1 and 2 are paired with multiple outputs. Therefore, G is not a function.
H = {(1,3) (2,6) (3,9), ..., (n, 3n), ... }
In relation H, each input n is paired with an output value of 3n. Since every input has a unique output, there are no repetitions. Therefore, H is a function.
To summarize:
F is a function.
G is not a function.
H is a function.