A relation R from A to B is given by a rule. Write R in roster form, find its domain, co-domain and range, and draw its arrow diagram.

1. 1 · Write what is given and what is to be found. Copy A, B and the rule for R.
2. 2 · Write the formula or theorem. R ⊆ A × B; domain = first coordinates, range = second coordinates.
3. 3 · Apply the rule. Take each element of A in turn. Keep a pair only if its partner is in B.
4. 4 · Write R in roster form. List the pairs inside braces, e.g. R = {(1, 2), (2, 5), ...}.
5. 5 · Name the three sets.
   • Domain: the first coordinates.
   • Co-domain: the whole set B.
   • Range: the second coordinates.
6. 6 · Draw the arrow diagram. Two ovals labelled A and B, elements inside, one arrow for each pair, labelled R.
7. 7 · Check and box the answer. Check that the range is a subset of the co-domain, then box R and the three sets.

Scoring tip: Write the co-domain in full even when some elements get no arrow. Examiners check that you know the range and co-domain can differ.