Question

Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then

Answer 1

atleast one of the sets Si is an ininite set

Answer 2

Answer:

If S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪  to Sn = S then atleast one of the sets Si is an ininite set

Step-by-step explanation:

Given:

• S be an infinite set
• S1, S2, S3, to Sn be sets
• S1 ∪S2 ∪S3∪ to Sn = S

Solution:

For S to be infinite set, atleast one of sets Si must be infinite

If all Si were finite, then S will also be finite.

Finite set

• Sets with a finite/countable number of members are referred to as finite sets.
• Due to their ability to be numbered, finite sets are also known as countable sets.
• If the elements of this set have a finite number of members, the operation will run out of elements to list.

Infinite set:

• The number of elements in a set cannot be counted and we are unable to describe it in roster form, a set that is not finite is referred to as an infinite set.
• Three dots (ellipses) are used to depict the elements of an infinite set, which symbolises the set's infinity.

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