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Pairs of Sets

The relations are stated between the pairs of sets. Learn to state, giving reasons whether the following sets are equivalent or equal, disjoint or overlapping.

Equal Set:

Two sets A and B are said to be equal if all the elements of set A are in set B and vice versa. The symbol to denote an equal set is =.

A = B means set A is equal to set B and set B is equal to set A.

For example;

A = {2, 3, 5}

B = {5, 2, 3}

Here, set A and set B are equal sets.

Equivalent Set:

Two sets A and B are said to be equivalent sets if they contain the same number of elements. The symbol to denote equivalent set is ↔.

A ↔ means set A and set B contain the same number of elements.

For example;

A = {p, q, r}

B = {2, 3, 4}

Here, we observe that both the sets contain three elements.

Notes:

Equal sets are always equivalent.

Equivalent sets may not be equal.

Disjoint Sets:

Two sets A and B are said to be disjoint, if they do not have any element in common.

For example;

A = {x : x is a prime number}

B = {x : x is a composite number}.

Clearly, A and B do not have any element in common and are disjoint sets.

Overlapping sets:

Two sets A and B are said to be overlapping if they contain at least one element in common.

For example;

• A = {a, b, c, d}

B = {a, e, i, o, u}

• X = {x : x ∈ N, x < 4}

Y = {x : x ∈ I, -1 < x < 4}

Here, the two sets contain three elements in common, i.e., (1, 2, 3)

The above explanations will help us to find whether the pairs of sets are equal sets or equivalent sets, disjoint sets or overlapping sets.