Equal and equivalent sets, definitions, and examples

A set is a collection of well-defined distinct objects of the same kind. For example, a set A ={prime numbers less than 15}. i.e A={2, 3, 5, 7, 11, 13}. A set is represented by a Capital letter, A, B, P, Q, etc. A set contains objects or elements or members in a curly bracket { }. In this article, we are going to discuss equal and equivalent sets.

Equal and equivalent sets, definitions, and examples

Equal and equivalent sets

Dealing with equal and equivalent sets, if care is not taken can be confusing but this article will give a clear picture of equal and equivalent sets.

What are equal sets

Equal set: if two sets have the same members then they are said to be equal sets. For example, if set A={a, e, i, o, u} and set B={o, i, u, a, e}. In this case, set A = B since they have the same members. In an equal set, the arrangements of the members of the set do not matter but they must have the same members. Also if set Q={2, 4, 6, 8, 10} and set P={2, a, 10, 6, 4}. Then a = 8 since set Q = P.

What are equivalent sets

Equivalent sets: if two sets have the same number of members or elements, then they are said to be equivalent. For example, if Set D={2, 3, 5, 7} and set E={22, 24, 26, 28}. Then we say set D is equivalent to set E since they both have four (4) members. Also set G={2, 4, 6, 8, 10} and set H={1, 3, 5, 7, 9}. Then set G is equivalent to set H since they both have five (5) elements.

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Difference between equal and equivalent sets

Two sets are said to be equal if they both have the same members while in an equivalent set, two sets are said to be equal if they both have the same number of elements.

Practice the questions below

Which of the following sets are equal sets and which ones are equivalent sets?

a) A={1, 3, 5, 7, 9, 11, 13}

B={11, 9, 3, 1, 5, 7, 13}

b) G={g, h, j, k, l}

H={1, 2, 3, 4, 5}

c) Q={x: 1 ≤ x ≤ 6}

P={1, 2, 3, 4, 5, 6}

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