Practice Element in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

An individual object that belongs to, or is a member of, a given set — either it is in the set or it is not.

An element is simply one item inside the collection — either it is in, or it is out. There is no "partially in."

easy

Let A = \{3, 7, 11, 15\}. Determine whether 7 \in A, \{7\} \in A, and 10 \notin A.

medium

Let B = \{\emptyset, \{1\}, \{2, 3\}\}. Which of the following are true? (a) \emptyset \in B, (b) 1 \in B, (c) \{1\} \in B, (d) \{2,3\} \subseteq B.

easy

Let S = \{1, 2, 3, 4, 5\}. Fill in each blank with \in or \notin: (a) 3 \;\square\; S, (b) 6 \;\square\; S, (c) 0 \;\square\; S.

medium

Let T = \{x \in \mathbb{Z} : x^2 < 10\}. List all elements of T and state |T|.