Question

using a venn diagram, find the no. of subsets of a given set and verify that a set has 'n' number of elements, the total number of subsets is 2^n​

Answer 1

There is no Venn Diagram given, so I will answer the second.

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Question: Verify that a set has 'n' number of elements, the total number of subsets is 2ⁿ.

Solution: Use events.

1st element: Choose or not (2 events)

2nd element: Choose or not (2 events)

So on... Until the last element

nth element: Choose or not (2 events)

Since these are independent events, we use multiplication.

There are 2×2×...2=2ⁿ events.

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Since the events are choosing the elements,

it is to say 2ⁿ elements.