Question

The total number of subsets of $\{1,2,6,7\}$ are?
1. 16
2. 8
3. 64
4. 32

Answer 1

Hint: To solve this problem we need to have basic knowledge on the set concepts and also, we need to have the knowledge about subsets and power sets and in here in this problem we have been given to find out the total number of subsets the given set has. so, for that we need to find out all the subsets of the given set first.

Complete step by step solution:
We know that, for a set containing n elements, the total number of subsets is ${{2}^{n}}$.
Consider $\{1,2,6,7\}$ , which has $4$ elements.
$\therefore $here $n=4$
Hence the total number of the subset the given set contains is ${{2}^{4}}=16$.
Thus, the total number of subsets of the given set $\{1,2,6,7\}$ is $16$.
So the answer is option $(1)$.
The given problem can be solved as follows by directly substituting the formula for finding the subsets to the given set.

So, the correct answer is “Option 1”.

Note: The student can solve the given problem from another method by finding all the subsets of the given set and then by counting all that could get the total numbers of subsets of the given set. Which is actually asked in the question to find out. The student should be known for exponent calculations and also the student must have the knowledge of the formulas given out in their syllabus for solving these kinds of problems. One should find the total number of subsets including the null set also.