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Online Quiz (Worksheet A B C D)

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High School Mathematics
7.9 Important Points in Sets

1. A set is a collection well defined objects.

2. A given object must be either belong to the set or not belong to it.

3. If an object (or element) belong to the set, we use the symbol '' to denote "belongs to " or "is a member of" or "is an element of".
"" is used to denote "does not belongs to" or "is not an element of".

4. By a well defined set, we mean that we must be able to tell whether a given object belong to a collection or not.

5. n(A) denotes the number of elements in a finite set A. It is called the cardinal number of A.

6. For any two finite sets A and B,
n(A B) = n(A) + n(B) - n(A B).

7. For any three finite sets A, B and C,
n(A B C) = n(A) + n(B) + n(C) - n(A B) - n(A C) - n(B C) + n(A B C).

Properties of Sets:

8. A B = B A. (Commutative property in union of sets)

9. A A = A. (Idempotent law under union)

10. A j = A, where j is empty set (Identity law)

11. A m = m, m is a universal set (Identity law)

12. A B = B A (Commutative law under intersection)

13. A A = A,(Idempotent law under intersection)

14. A j = j (Identity law under intersection)

15. A m = A (Identity law under intersection)

16. (A B) C = A (B C) (Associative law under union of sets)

17. (A B) C = A (B C) (Associative law under intersection of sets)

18. A (B C) = (A B) (A C) (Distributive law)

19. A (B C) = (A B) (A C). (Distributive law)

20. (A B)' = A' B' (De Morgan's law)

21. (A B)' = A' B' (De Morgan's law)

22. j' = m and m' = j (Complement laws)

Q 1: A' A = _____.

Q 2: (A')' = _____.

Q 3: j' = _____.

Q 4: A - (B C)
(A - B) (A - C)
(A - B) (A - C)

Q 5: m' = ____.

Q 6: A (B C) = ______.

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Question 8: This question is available to subscribers only!

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