Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
If a set S has 4 elements, how many elements are there in its power set P(S)?
8
12
16
32
16
Remember the powers of 2 for small integers: 2┬╣=2, 2┬▓=4, 2┬│=8, 2тБ┤=16. Just evaluate 2 raised to the power of the number of elements.
The set S consists of 4 elements, meaning the cardinality of set S is n = 4.
тИгP(S)тИг=2n
Remember the powers of 2 for small integers: 2┬╣=2, 2┬▓=4, 2┬│=8, 2тБ┤=16. Just evaluate 2 raised to the power of the number of elements.
Many students confuse the power set formula 2n with n2 or 2n, leading to incorrect answers like 8 or 16 depending on the error.
Identify cardinality
The number of elements in set S is given as n=4.
n=4
Apply the power set formula
The number of elements in the power set P(S) is defined by the formula 2n. Substituting n=4 into the formula, we get 24.
тИгP(S)тИг=24
Calculate the result
Evaluating the exponent, 24=2├Ч2├Ч2├Ч2=16.
24=16
C is correct because the number of subsets of a set with 4 elements is 24, which equals 16.
This concept is foundational for understanding the total number of relations possible between two sets, which is given by 2m├Чn where m and n are the cardinalities of the two sets.