Equal Set

Equal Set:-

• A = {Sachin, Dravid, Kohli}
• B = {Dravid, Sachin, Dhoni}
• C = {Kohli, Dravid, Sachin}

Two sets A and C are said to be equal if every element in A belongs to C and
every element in C belongs to A. If A and C are equal sets, than we write A = C.

we can also write that if B ⊂ A and A ⊂ B ⇔A = B. Here ⇔ is the
isymbol fortwo way implication and is usually read as, if and only if
(briefly written as “iff”).

1. A = {1, 2, 3}; B = {The first three natural numbers}


2. C = {a, b, c, d}; D = {d, c, a, b}


3. E = {a, e, i, o, u}; F = {set of vowels in English Alphabet}

Note:If A and B contain the same elements, they are equal i.e. A = B.
By thisobservation we can say that “Every set is subset of itself”.

Example:Consider the sets φ, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}.
Insert the symbol ⊂ or ⊄ between each of the following pair of sets.
(i) φ ….. B (ii) A ….. B (iii) A ….. C (iv) B ….. C


Solution :
(i) φ ⊂ B, as φ is a subset of every set.
(ii) A ⊄ B, for 3 ∈ A but 3 ∉ B.
(iii) A ⊂ C as 1, 3 ∈A also belong to C.
(iv) B ⊂ C as each element of B is also an element of C.