Let $P=\{1,2,3, \ldots, 100\}$ be the number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is

JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Analyzing +4 | -1

Let

P=\{1,2,3, \ldots, 100\}

be the number of non-empty subsets

A

S

such that the product of elements in

A

is even is

View answer and explanation

Correct option: A

2^{50}\left(2^{50}-1\right)

Option A (

2^{50}(2^{50}-1)

) is correct because it calculates the total number of non-empty subsets minus the number of subsets containing only odd numbers.

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S

2 a_1 a_2 a_3 \ldots . . a_{2006}

a_1, a_2, a_3, \ldots ., a_{2006}

S

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

b N \cap c N=d N

a, b, c \in N

b, c

A=\{x: x

\}

B=\{x: x

A-B

F(n)

n

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

40 \%

A, 20 \%

10 \%

C

A

C

4 \%

A

C

2 \%

A