Worksheet on Union and Intersection of Sets

Worksheet on union and intersection of sets will help us to practice different types of questions using the basic ideas of the 'union' and 'intersection' of two or more sets.

1. State whether the following are true or false:

(i) If A = {5, 6, 7} and B = {6, 8, 10, 12}; then A ∪ B = {5, 6, 7, 8, 10, 12}.

(ii) If P = {a, b, c} and Q = {b, c, d}; then p intersection Q = {b, c}.

(iii) Union of two sets is the set of elements which are common to both the sets.

(iv) Two disjoint sets have atleast one element in common.

(v) Two overlap sets have all the elements common.

(v) If two given sets have no elements common to both the sets, the sets are said to me disjoint.

(vii)  If A and B are two disjoint sets then A ∩ B = { }, the empty set.

(viii) If M and N are two overlapping sets then intersection of two sets M and N is not the empty set.


2. Let A, B and C be three sets such that:

Set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15} and set C = {1, 4, 7, 10, 13, 16}.

Find:

(i) A ∪ B

(ii) A ∩ B

(iii) B ∩ A

(iv) B ∪ A

(v) B ∪ C

(vi) Is A ∪ B = B ∪ A?

(vii) Is B ∩ C = B ∪ C?


3. If A = {1, 3, 7, 9, 10}, B = {2, 5, 7, 8, 9, 10}, C = {0, 1, 3, 10}, D = {2, 4, 6, 8, 10}, E = {negative natural numbers} and F = {0}

Find:

(i) A ∪ B

(ii) E ∪ D

(iii) C ∪ F

(iv) C ∪ D

(v) B ∪ F

(vi) A ∩ B

(vii) C ∩ D

(viii) E ∩ D

(ix) C ∩ F

(x) B ∩ F

(xi) (A ∪ B) ∪ (A ∩ B)

(xii) (A ∪ B) ∩ (A ∩ B)


4. If A = {2, 3, 4, 5}, B ={c, d, e, f} and C = {4, 5, 6, 7};

Find:

(i) A ∪ B

(ii) A ∪ C

(iii) (A ∪ B) ∩ (A ∪ C)

(iv) A ∪ (B ∩ C)

(v) Is (A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C)?


5. If A = {a, b, c, d}, B = {c, d, e, f} and C = {b, d, f, g};

Find:

(i) A ∩ B

(ii) A ∩ C

(iii) (A ∩ B) ∪ (A ∩ C)

(iv) A ∩ (B ∪ C)

(v) Is (A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)?


Answers for the worksheet on union and intersection of sets are given below to check the exact answers of the above set of questions.


Answers:


1.  (i) True

 (ii) True

(iii) False

(iv) False

(v) False

(vi) True

(vii) True

(viii) True


2. (i) {2, 3, 4, 6, 7, 9, 10, 12, 15}

(ii) { }

(iii) {6, 12}

(iv) {2, 3, 4, 6, 8, 9, 10, 12, 15}

(v) {{1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16}

(vi) Yes, A ∪ B = B ∪ A

(vii) No, B ∩ C ≠ B ∪ C


3. (i) {1, 2, 3, 5, 7, 8, 9, 10}

(ii) {2, 4, 6, 8, 10}

(iii) {0, 1, 3, 10}

(iv) {0, 1, 2, 3, 4, 6, 8, 10}

(v) {0, 2, 5, 7, 8, 9, 10}

(vi) {7, 9, 10}

(vii) {10}

(viii) ∅

(ix) {0}

(x) ∅

(xi) {1, 2, 3, 5, 7, 8, 9, 10,

(xii) {7, 9, 10}


4. (i) {1, 2, 3, 4, 5, 7}

(ii) {2, 3, 4, 5, 6, 7}

(iii) {2, 3, 4, 5, 7}

(iv) {2, 3, 4, 5, 7}

(v) Yes, (A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C)


5. (i) {c, d}

(ii) {b ,d}

(iii) {b, c, d}

(iv) {b , c, d}

(v) Yes, (A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)

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