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Given that N ...

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Given that N = {1, 2, 3, …, 100}, then (i) Write the subset A of N, whose elements are odd numbers. (ii) Write the subset B of N, whose elements are represented by x + 2, where x ∈ N.

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Q. Assertion :A set

X

n

elements. Two subsets

A

B

X

are chosen at random. The probability that

A

B

have same number of elements is

\frac{1.3.5... (2 n - 1)}{2^{n} (n!)}

{(^{n} C_{0})}^{2} + {(^{n} C_{1})}^{2} + . . . + {(^{n} C_{n})}^{2} = \frac{2^{n} (1.3.5... (2 n - 1))}{n!}

Q. The number of subsets of a set containing n elements is
(a) n
(b) 2ⁿ − 1
(c) n²
(d) 2ⁿ

A

n \times n

matrix whose elements are all

^{'} 1^{'}

B

n \times n

matrix whose diagonal elements are all

n

and other elements are

^{'} n - r^{'}

(B - r I) [B - (n^{2} - n r + r) I] = 0

because Reason:

A^{2}

is a scalar multiple of

A

.

n

be a natural number and

X = {1, 2, . . . . . ., n}

A

B

X,

A Δ B

to be the set of all those elements of

X

which belong to exactly one of

A

B .

F

be a collection of subsets of

X

such that for any two distinct elements

A

B

F

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F

2^{n - 1}

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Q. Assertion :The number of non empty subsets of the set

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15

. Reason: Number of non empty subsets of a set having

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