Practice Element in Math

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

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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."

Showing a random 20 of 50 problems.

Example 1

hard
Element X has Z=79Z = 79. List its proton count, its likely conductivity, and one common use.

Example 2

challenge
For A={∅,{∅}}A=\{\emptyset,\{\emptyset\}\}, determine the truth of: ∅∈A\emptyset\in A, {∅}∈A\{\emptyset\}\in A, {∅}⊆A\{\emptyset\}\subseteq A.

Example 3

easy
About how many elements are currently known?

Example 4

easy
Is 22 an element of {1,2,3}\{1,2,3\}? Write the symbol.

Example 5

medium
Stainless steel is made of iron, chromium, nickel, and carbon blended together. Is it an element?

Example 6

challenge
Why is the periodic table organized by atomic number (ZZ) rather than by atomic mass?

Example 7

medium
Is {a}∈{{a},{b}}\{a\} \in \{\{a\},\{b\}\}? Is a∈{{a},{b}}a \in \{\{a\},\{b\}\}?

Example 8

medium
Given A={1,2}A=\{1,2\} and B={2,3}B=\{2,3\}, list elements of A∪BA\cup B and confirm 2∈A∩B2\in A\cap B.

Example 9

challenge
Helium (He\text{He}) is the second-most abundant element in the universe but rare in Earth's atmosphere. Suggest one reason.

Example 10

easy
What single property is shared by every atom of a given element?

Example 11

hard
Why is hydrogen (H) sometimes placed in group 1 and sometimes in group 17 on the periodic table?

Example 12

easy
Two atoms have 6 and 7 protons. Are they the same element?

Example 13

easy
Is 00 an element of the set of natural numbers {1,2,3,… }\{1,2,3,\dots\} as written here?

Example 14

hard
Compare an element (e.g., O2\text{O}_2) and a compound (e.g., O3\text{O}_3 + ozone) — both contain only oxygen. Why is O3\text{O}_3 still considered an element?

Example 15

easy
Let S={1,2,3,4,5}S = \{1, 2, 3, 4, 5\}. Fill in each blank with ∈\in or ∉\notin: (a) 3  □  S3 \;\square\; S, (b) 6  □  S6 \;\square\; S, (c) 0  □  S0 \;\square\; S.

Example 16

easy
Which symbol is correct: 2 ? {1,2,3}2 \,?\, \{1,2,3\} versus {2} ? {1,2,3}\{2\} \,?\, \{1,2,3\}?

Example 17

hard
Element Q exists as a colorless gas that does not react with anything under normal conditions. To which family does it likely belong?

Example 18

medium
For A={1,{2},3}A=\{1,\{2\},3\}, decide: is 2∈A2 \in A? Is {2}∈A\{2\}\in A?

Example 19

easy
Is 11 the same as {1}\{1\}?

Example 20

hard
Which element has the highest natural abundance in the Earth's crust by mass?
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Related Concepts

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