Which of the following are sets? Justify your answer.The collection of all whole numbers less than 10. - Noon Academy

Which of the following are sets? Justify your answer.
The collection of all whole numbers less than 10.

RS Agarwal Class 11 Maths Sets

Which of the following are sets? Justify your answer.
The collection of all whole numbers less than 10.

Whole numbers are 0, 1, 2, 3, …
Whole numbers less than 10 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
As the collection of all whole numbers, less than 10 is known and can be counted, i.e. well – defined.
∴, this is a set.

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More Material

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Prove that A – B = A ∩ B.’

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Prove that A ∩ (A B)’ = φ

If A = {3, {2}}, find P(A).

If A = {5, 6, 7}, find P(A).

Let A = {x : x = 6n N) and B = {x : x = 9n, n ε N}, find A ∩ B.

If A ⊂ B, show that (B’ – A’) = φ.

If A ⊂ B, prove that B’ ⊂ A’.

If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B). Hint n(B) = n(B – A) + n(A ∩ B) ⇒ n(A ∩ B) = (39 – 13) = 26.

If A and B are two sets such that n(A) = 23, n(b) = 37 and n(A – B) = 8 then find n(A ∪ B). Hint n(A) = n(A – B) + n(A ∩ B) n(A ∩ B) = (23 – 8) = 15.

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