Worked Example 1
Write the set of factors of 12 by the listing method, and state n(A).
Find them in pairs1 × 12, 2 × 6, 3 × 4. Every factor has a partner, so pairs stop you missing one.
Write the setA = {1, 2, 3, 4, 6, 12}
Cardinal numbern(A) = 6. This is a plain number, not a set, so no brackets.
Worked Example 2
List all the subsets of B = {a, b, c} and check the count.
Work by size, not at random{ }, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}
Count1 + 3 + 3 + 1 = 8, and 2³ = 8, which agrees.
Do not forget the two odd onesThe empty set is a subset of every set, and every set is a subset of itself. Leaving those out gives 6 instead of 8.
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