Exercises: Universal Sets, Complement Sets, and Subsets

Equivalent sets only — they merely share the same count of elements.

Unequal sets — the two labels A and B mean they must be different.

Equal sets — they contain exactly the same elements.

1, 2, 3, 4, without any brackets around the numbers.

{1, 2, 3, 4}, using curly brackets around the four distinct numbers.

{1, 1, 2, 3, 4}, listing 1 twice for emphasis.

U stays exactly the same set, {oranges, mangoes, bananas, pineapples}, no matter what the context is.

U can change, because the universal set depends on the context being considered — a market likely has more kinds of fruit than one basket.

U becomes an empty set, because a market is a different place from a basket.

{1, 3, 5, 7, 9, 11, 13} — all odd numbers, including some beyond U.

{2, 4, 6, 8, 10} — the same elements as A.

{1, 3, 5, 7, 9} — all the elements of U that are not in A.

{a, b, c, d, e} — the same as the universal set U.

{c, d, e} — all the elements of U that are not in B.

{a, b} — the same as set B.

No, because C has fewer elements than U, so it cannot be a subset.

No, because C would need to equal U exactly to be considered a subset.

Yes, C ⊂ U — every element of C (2, 4, 6) is also an element of U.