Question

Using a Venn diagram find the number of a subset of a given set and verify that if a set has n number of elements, the total number of subsets is 2n​

Answer 1

Therefore, the total number of subsets is
`2^(n)`​ if a set has n elements

Let's consider a set with n elements. To find the total number of subsets, we can use the formula
`2^(n)`, where n is the number of elements in the set. This formula accounts for all possible combinations of elements, including the empty set and the set itself.

Now, let's verify this formula using a Venn diagram for a set with three elements. The set will be {A, B, C}. The possible subsets are:

Empty set: {}

Single-element subsets: {A}, {B}, {C}

Two-element subsets: {A, B}, {A, C}, {B, C}

Three-element subset: {A, B, C}

Now, let's count the subsets and verify if it matches the formula
`2^(n)`:

`2^(3)` = 8

The subsets we listed above indeed total to 8, confirming the formula for a set with three elements.

Therefore, the total number of subsets is
`2^(n)`​ if a set has n elements