What are the two basic properties of sets?

The two basic properties to represent a set are explained below using various examples.

**1. The change in order of writing the elements does not make any changes in the set.**

In other words the order in which the elements of a set are written is not important. Thus, the set {a, b, c} can also be written as {a, c, b} or {b, c, a} or {b, a, c} or {c, a, b} or {c, b, a}.

For Example:

Set A = {4, 6, 7, 8, 9} is same as set A = {8, 4, 9, 7, 6}

i.e., {4, 6, 7, 8, 9} = {8, 4, 9, 7, 6}

Similarly, {w, x, y, z} = {x, z, w, y} = {z, w, x, y} and so on.

**2. If one or many
elements of a set are repeated, the set remains the same.**

In other words the elements of a set should be distinct. So, if any element of a set is repeated number of times in the set, we consider it as a single element. Thus, {1, 1, 2, 2, 3, 3, 4, 4, 4} = {1, 2, 3, 4}

The set of letters in the word ‘GOOGLE’ = {G, O, L, E}

For Example:

The set A = {5, 6, 7, 6, 8, 5, 9} is same as set A= {5, 6, 7, 8, 9}

i.e., {5, 6, 7, 6, 8, 5, 9} = {5, 6, 7, 8, 9}

In general, the elements of a set are not repeated. Thus,

(i) if T is a set of letters of the word ‘moon’: then T = {m, o, n},

There are two o’s in the word ‘moon’ but it is written in the set only once.

(ii) if U = {letters of the word ‘COMMITTEE’}; then U = {C, O, M, T, E}

Solved examples using the properties of sets:

**1.** Write the set
of vowels used in the word ‘UNIVERSITY’.

**Solution:**

Set V = {U, I, E}

**2.** For each
statement, given below, state whether it is true or false along with the
explanations.

(i) {9, 9, 9, 9, 9, ……..} = {9}

(ii) {p, q, r, s, t} = {t, s, r, q, p}

**Solution:**

(i) {9, 9, 9, 9, 9, ……..} = {9}

True, since repetition of elements does not change the set.

(ii) {p, q, r, s, t} = {t, s, r, q, p}

True, since the change in order of writing the elements does not change the set.

● **Set Theory**

●** Sets**

**● **Subset

**7th Grade Math Problems**

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