Practice Operation Closure in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A set is closed under an operation if performing that operation on members of the set always produces a result that is also in the set. For example, integers are closed under addition.
Adding two whole numbers always gives a whole number—closed under addition.
Showing a random 20 of 50 problems.
Example 1
mediumIs the set closed under multiplication? Check all products.
Example 2
easyAre the negative integers closed under addition?
Example 3
hardIs the set of invertible real matrices closed under multiplication?
Example 4
easyAre the multiples of 3 closed under multiplication?
Example 5
mediumAre the powers of closed under addition?
Example 6
challengeIs the set of perfect squares closed under multiplication? Justify.
Example 7
mediumAre the multiples of 5 closed under addition? Justify.
Example 8
easyAre the odd integers closed under addition? (yes/no)
Example 9
mediumAre the whole numbers closed under subtraction? Give a counterexample if not.
Example 10
easyAre the whole numbers closed under multiplication? (yes/no)
Example 11
mediumIs division by zero a reason that nonzero rationals are 'almost' closed under division? Explain in one line.
Example 12
challengeShow that the set of odd integers is closed under multiplication but not addition.
Example 13
challengeShow that the set is closed under multiplication.
Example 14
easyAre the multiples of 3 closed under addition?
Example 15
easyTrue or false: is closed under both addition and multiplication.
Example 16
mediumAre the negative integers closed under multiplication? Justify.
Example 17
easyIs the set of integers closed under division? (yes/no)
Example 18
easyIs the set of integers closed under subtraction?
Example 19
mediumIs the set of irrational numbers closed under addition? Give reasoning.
Example 20
easyGive one counterexample showing positive integers are not closed under subtraction.