Let S be an infinite set and S1- S2- Sn be sets such that S1 - S2 - Sn-S- Then

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Standard VII

Mathematics

Union

Let S be an i...

Question

Let $S$ be an infinite set and $S_{1}, S_{2}, \dots \dots S_{n}$ be sets such that $S_{1} \cup S_{2} \cup \dots \cup S_{n} = S$ . Then

At least one of the sets

S_{1}

is a finite set

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Not more than one of the sets

S_{1}

can be finite

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At least one of sets

S_{1}

is infinite

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Not more than one the sets

S_{1}

is an infinite set.

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Solution

The correct option is C At least one of sets $S_{1}$ is infinite
$S = S_{1} \cup S_{2} \cup S_{3} \cup \dots \cup S_{n}$
For $S$ to be infinite set, atleast one of sets $S_{i}$ must be infinite, since if all $S_{i}$ were finite, then $S$ will also be finite.

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Q. Let X be the set of first 100 natural numbers. Sets S1 and S2 are subsets of X such that each of them has more than zero elements and no common element. If the maximum number of elements in S1 = x1, in S2 = y1 and minimum no. of elements in S1 = x2, in S2 = y2 then:
Suppose the union of sets S1 and S2 is X and S1, S2 have the same number of elements. If elements from S1 and S2 are chosen randomly, it was found that by exchanging two elements of S1 with two elements of S2, every element of S1 was greater than that of S2. Find the no. of sets S1 that can be formed.

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Let S be an infinite set and S1, S2,……Sn be sets such that S1∪S2∪⋯∪Sn=S. Then

The correct option is C At least one of sets S1 is infiniteS=S1∪S2∪S3∪…∪Sn For S to be infinite set, atleast one of sets Si must be infinite, since if all Si were finite, then S will also be finite.

Let $S$ be an infinite set and $S_{1}, S_{2}, \dots \dots S_{n}$ be sets such that $S_{1} \cup S_{2} \cup \dots \cup S_{n} = S$ . Then

The correct option is C At least one of sets $S_{1}$ is infinite
$S = S_{1} \cup S_{2} \cup S_{3} \cup \dots \cup S_{n}$
For $S$ to be infinite set, atleast one of sets $S_{i}$ must be infinite, since if all $S_{i}$ were finite, then $S$ will also be finite.