Practice Set in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A well-defined collection of distinct, unordered objects called elements, described either by listing or by a membership rule.
Think of a set as a bag that can hold anything — numbers, names, shapes — but with two strict rules: no duplicates allowed and the order in which items sit inside the bag does not matter.
Showing a random 20 of 50 problems.
Example 1
mediumWrite in roster form (positive divisors only).
Example 2
mediumSet is described as 'all integers with '. List by roster.
Example 3
mediumWrite in roster form.
Example 4
easyIs the same thing as the number ?
Example 5
hardHow many subsets does a set with elements have?
Example 6
easyTrue or false: the set of letters in 'EYE' has elements.
Example 7
challengeProve that if sets and satisfy and , then .
Example 8
easyIs the same set as ?
Example 9
challengeSet contains its own number of elements rule: has exactly elements. If a set satisfies , what must be true about ?
Example 10
mediumList the subset of consisting of perfect squares.
Example 11
easyLet . List all elements of and state the cardinality .
Example 12
easyLet . Determine whether and whether .
Example 13
mediumWrite the set in roster notation.
Example 14
mediumConvert to roster form.
Example 15
mediumTrue or false: has the same elements as .
Example 16
easyIs ?
Example 17
easyAre the sets and equal? Explain.
Example 18
easyLet . Is ? Is ?
Example 19
mediumAre the sets and equal?
Example 20
mediumIs the collection of 'the three best movies ever' a well-defined set?