Question

State whether the following statement is true or false. Give reason to support your answer.
\left\\{ {a,b,c} \right\\} and $\\{ 1,2,3\\}$ are equivalent sets.
(A) True
(B) False

Answer 1

In this question, we are given a statement.
We have to find out whether the given statement is true or false.
We have to first find out the definition of an equivalent set. Then comparing the given two sets by using the definition we will get the required solution.

Complete step-by-step solution:
It is given that, \left\\{ {a,b,c} \right\\} and $\\{ 1,2,3\\}$ are equivalent sets.
We need to find out whether the following statement is true or false.
An equivalent set is a set with an equal number of elements. The sets don’t need to have the same exact elements, just an equivalent number of elements.
\left\\{ {a,b,c} \right\\} contains three elements a, b, c.
$\\{ 1,2,3\\}$ contains three elements $1,2,3$ .
Thus, we get, both sets contain exactly three distinct elements.
Hence, the sets are equivalent.

Therefore, (A) is the correct option.

Note: Set:
A set in mathematics is a collection of well-defined elements and the number of elements in the finite set is known as the cardinal number of a set.
For example: the set, S = \left\\{ {a,b,c,d,e} \right\\} contains five elements.
Equivalent set:
If the number of elements in the two different sets are the same, then they are called equivalent sets. The order of the sets is insignificant. It is represented as:
$n\left( A \right) = n\left( B \right)$
Where A and B are two different sets with the same number of elements.
When we have two sets that have the exact same elements, we call them equal sets. The order of the elements in the set does not matter. Only the elements of the set matters.
For example: the set, S = \left\\{ {a,b,c,d,e} \right\\} and P = \left\\{ {c,b,a,e,d} \right\\} are equal sets.
But, let, S = \left\\{ {a,b,c,d,e} \right\\} and P = {January, February, March, April, May}, even though sets S and P have completely different elements they are equivalent because they both contain five elements but they are not equal.