The number of subsets of {1, 2, 3, ldots, 9} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of subsets of the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ is $2^n$,where $n=9$. Total subsets $= 2^9 = 512$. We want to find the

Vedclass · Accepted Answer

$496$

Vedclass · Answer

(C) The total number of subsets of the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ is $2^n$,where $n=9$. Total subsets $= 2^9 = 512$. We want to find the number of subsets that contain at least one odd number. It is easier to calculate the complement: the number of subsets that contain $NO$ odd numbers. $A$ subset contains no odd numbers if and only if all its elements are even. The even numbers in the set are $\{2, 4, 6, 8\}$. The number of subsets formed using only these even numbers is $2^4 = 16$. These $16$ subsets include the empty set $\emptyset$. Therefore,the number of subsets containing at least one odd number is Total subsets $-$ Subsets with only even numbers. Required number $= 512 - 16 = 496$.

The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

Similar Questions

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \text{ is a prime number} \}$

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \in N \text{ and } 2x + 1 > 10 \}$

If $A$ and $B$ are two sets,then $A \cap (A \cap B)^c$ is equal to:

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$,$A = \{1, 2, 5\}$,and $B = \{6, 7\}$. Find $A \cap B'$.

Draw an appropriate Venn diagram for the following: $(A \cup B)'$

Vedclass Test Series

Exam Paper Generator

Online Exam Module