Arrow diagram discrete math question

Question

So in this arrow diagram example, the function G is defined as C --> D with the sets represented below:

C = {1, 2, 3, 4} and D = {a, b, c, d}

Elements, **1, 2, 3,** and **4** from set C all correspond to element **C** from set D.

So is the domain: { 1, 2, 3, 4} and codomain: { a, b, c, d} ?

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Also, does G (1) simply mean: G(1) = C?

What about, G(2), G (3), and G (4)?

Would the correct solution be

G (2) = C

G (3) = C

G (4) = C

Or is there a fancier way of writing this in discrete math? Neither youtube nor the textbook covers any examples for my second portion of the question.

Answer 1

Seems correct to me. The domain and codomain are correct (but note that the range would be {c} and not the whole set)

>Also, does G (1) simply mean: G(1) = C?

>What about, G(2), G (3), and G (4)?

>Would the correct solution be

>G (2) = C

>G (3) = C

>G (4) = C

Small error. It'll be c and not C. C is the name of the set, while c is an element. Writing G(1) = C is incorrect. Writing G(1) = c, however, is correct. Otherwise yes, as all elements from C map to c in D, any input into the function from set C will only yield c as the output, as you have shown