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Question

Consider the following statements :
1. N(BZ)=(NB)Z for any subset B of R, where N is the set of positive integers, Z is the set of integers, R is the set of real numbers.

2. Let A={nN:1n24,n is a multiple of 3}. There exists no subset B of N such that the number of elements in A is equal to the number of elements in B.

Which of the above statements is/are correct?

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor \(2\
)
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Solution

The correct option is A 1 only
(NB)Z=(NZ)(BZ)
=N(BZ)
(1) is correct.

A={3,6,9,12,15,18,21,24}
and there exist subset B of N such that the number of elements in A is equal to the number of elements in B.
Clearly, we can find BN such that n(A)=n(B)
(2) is not correct.

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