Practice Element in Math

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

Worksheet PDF Free Answer-key PDF Family

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 = 79

. List its proton count, its likely conductivity, and one common use.

Example 2

challenge

For

A=\{\emptyset,\{\emptyset\}\}

, determine the truth of:

\emptyset\in A

\{\emptyset\}\in A

\{\emptyset\}\subseteq A

Example 3

easy

About how many elements are currently known?

Example 4

easy

2

an element of

\{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 (

Z

) rather than by atomic mass?

Example 7

medium

\{a\} \in \{\{a\},\{b\}\}

? Is

a \in \{\{a\},\{b\}\}

Example 8

medium

Given

A=\{1,2\}

and

B=\{2,3\}

, list elements of

A\cup B

and confirm

2\in A\cap B

Example 9

challenge

Helium (

\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

0

an element of the set of natural numbers

\{1,2,3,\dots\}

as written here?

Example 14

hard

Compare an element (e.g.,

\text{O}_2

) and a compound (e.g.,

\text{O}_3

+ ozone) — both contain only oxygen. Why is

\text{O}_3

still considered an element?

Example 15

easy

Let

S = \{1, 2, 3, 4, 5\}

. Fill in each blank with

\in

\notin

: (a)

3 \;\square\; S

, (b)

6 \;\square\; S

, (c)

0 \;\square\; S

Example 16

easy

Which symbol is correct:

2 \,?\, \{1,2,3\}

versus

\{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\}

, decide: is

2 \in A

? Is

\{2\}\in A

Example 19

easy

1

the same as

\{1\}

Example 20

hard

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

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Related Concepts

Set Subset