Worksheet on disjoint sets and overlapping sets will help us to practice different types of questions to state whether the pairs of sets are disjoint or overlapping.

We know, if two sets are disjoint they do not have any common element and if two sets are overlapping they at least have one common element.

To answer the questions in the worksheet on disjoint sets and overlapping sets, read the above explanations carefully.

**1.** Find whether the sets P and Q are overlapping sets or disjoint sets:

(i) P = {10, 20, 30, 40};

Q = {15, 25, 35, 45};

(ii) P = {2, 4, 6, 8, 10};

Q = {1, 3, 5, 7, 8};

(iii) P = {S, U, N};

Q = {S, T, A, R};

(iv) P = {x : x is letter in the ‘FLOWER’};

Q = {x : x is letter in the ‘FLOOR’};

(v) P = {x : x is a factor of 24};

Q = {x : x is a factor of 33};

(vi) P = {x : x is a multiple of 7 between 1 and 50};

Q = {x : x is a multiple of 11 between 1 and 50};

** **

**2.** State, giving
reasons, which of the following pairs of sets are **disjoint sets** or **overlapping
sets**:

(i) A = {Girls with ages below 15 years} and

B = {Girls with ages above 15 years}

(ii) A = {Boys with ages above 20 years} and

B = {Boys with ages above 27 years}

(iii) A = {Naturals between 35 and 60} and

B = {Naturals between 50 and 80}

(iv) A = {Students of class X studying in California} and

B = {Students of class X}

(v) A = {Naturals numbers multiples of 3 and less than 30} and

B = {Natural numbers divisible by 4 and between 20 and 45}

(vi) A = {Letters in the word ‘MOON’} and

B = {Letters in the word ‘STAR’}

Answers for the worksheet on disjoint sets and overlapping sets are given below to check the exact answers of the above questions of the pairs of sets i.e. disjoint and overlapping.

**Answers:**

**1.** (i) Disjoint
sets

(ii) Overlapping sets

(iii) Overlapping sets

(iv) Overlapping sets

(v) Overlapping sets

(vi) Disjoint sets

**2.** (i) Disjoint
sets; as no girl can be of age below 15 years and also above 15 years

(ii) Overlapping sets; as boys above 27 years are also above 20 years

(iii) Overlapping sets; as naturals from 50 to 59 are common to both the sets.

(iv) Overlapping sets; as students of class X studying in California are common.

(v) Overlapping sets: as natural number 24 is common to both the sets.

(vi) Disjoint sets; as no letter is common to both the sets.

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