Let S be a set of consisting of 10 elements. The number of tuples of the form…
2021
Let S be a set of consisting of 10 elements. The number of tuples of the form (A,B) such that A and B are subsets of S, and A⊆B is ___________ .
Attempted by 490 students.
Show answer & explanation
Correct answer: 59049
Key idea: for each element of S there are three valid possibilities respecting A ⊆ B.
The element is in neither A nor B.
The element is in B but not in A.
The element is in both A and B.
Since the choices for distinct elements are independent, the total number of pairs (A,B) with A ⊆ B is 3^10 = 59049.
A video solution is available for this question — log in and enroll to watch it.