Sets word problems worksheets are much useful to the students who would like to practice word problems on set theory.

1) **In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken **** chemistry and physics course, and 14 had taken all the three courses.** Find how many had taken one course only.

2) **In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group. **(Assume that each student in the group plays at least one game.)

3) In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects.

Find the number of students who like

(i) Math only, (ii) Science only (iii) Either Math or Science (iv) Neither Math nor science

4) At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. Find the number of women doctors attending the conference.

**Problem 1 :**

In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only.

**Solution :**

**Step 1 :**

Let M, C, P represent sets of students who had taken mathematics, chemistry and physics respectively

**Step 2 :**

From the given information, we have

n(M) = 64 , n(C) = 94, n(P) = 58,

n(MnP) = 28, n(MnC) = 26, n(CnP) = 22

n(MnCnP) = 14

**Step 3 :**

From the basic stuff, we have

No. of students who had taken only **Math**

= n(M) - [n(MnP) + n(MnC) - n(MnCnP)]

= 64 - [28+26-14]

= 64 - 40

= 24

**Step 4 :**

No. of students who had taken only **Chemistry**

= n(C) - [n(MnC) + n(CnP) - n(MnCnP)]

= 94 - [26+22-14]

= 94 - 34

= 60

**Step 5 :**

No. of students who had taken only **Physics**

= n(P) - [n(MnP) + n(CnP) - n(MnCnP)]

= 58 - [28+22-14]

= 58 - 36

= 22

**Step 6 :**

Total no. of students who had taken **only one** course

= 24 + 60 + 22

= 106

**Hence, the total number of students who had taken only one course is 106 **

**Alternative Method (Using venn diagram)**

**Step 1 :**

Venn diagram related to the information given in the question:

**Step 2 :**

From the venn diagram above, we have

No. of students who had taken only math = 24

No. of students who had taken only chemistry = 60

No. of students who had taken only physics = 22

**Step 3 :**

Total no. of students who had taken only one course

= 24 + 60 + 22

= 106

**Hence, the total number of students who had taken only one course is 106**

Let us look at the next problem on "Sets word problems worksheets"

**Problem 2 :**

In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group. (Assume that each student in the group plays at least one game.)

**Solution :**

**Step 1 :**

Let F, H and C represent the set of students who play foot ball, hockey and cricket respectively.

**Step 2 :**

From the given information, we have

n(F) = 65 , n(H) = 45, n(C) = 42,

n(FnH) = 20, n(FnC) = 25, n(HnC) = 15

n(FnHnC) = 8

**Step 3 :**

From the basic stuff, we have

Total number of students in the group = n(FuHuC)

= n(F) + n(H) + n(C) - n(FnH) - n(FnC) - n(HnC) + n(FnHnC)

= 65 + 45 + 42 -20 - 25 - 15 + 8

= 100

**Hence, the total number of students in the group is 100**

**Alternative Method (Using venn diagram)**

**Step 1 :**

Venn diagram related to the information given in the question:

**Step 2 :**

Total number of students in the group

= 28 + 12 + 18 + 7 + 10 + 17 + 8

= 100

**Hence, the total number of students in the group is 100**

Let us look at the next problem on "Sets word problems worksheets"

**Problem 3 :**

In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects.

Find the number of students who like

(i) Math only, (ii) Science only (iii) Either Math or Science (iv) Neither Math nor science

**Solution :**

**Step 1 :**

Let M and S represent the set of students who like math and science respectively.

**Step 2 :**

From the information given in the question, we have

n(M) = 40, n(S) = 36, n(MnS) = 24

**Step 3 :**

**Answer (i) :** No. of students who like math only

= n(M) - n(MnS)

= 40 - 24

= **16**

**Step 4 :**

**Answer (ii) :** No. of students who like science only

= n(S) - n(MnS)

= 36 - 24

= **12**

**Step 5 :**

**Answer (iii) :** No. of students who like either math or science

= n(M or S)

= n(MuS)

= n(M) + n(S) - n(MnS)

= 40 + 36 - 24

= **52**

**Step 6 :**

**Answer (iv) :**

Total no. students who like any of the two subjects = n(MuS) = 52

No. of students who like neither math nor science

= 60 - 52

= **8**

**Let us look at the next problem on "Sets word problems worksheets"**

**Problem 4 :**

At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. Find the number of women doctors attending the conference.

**Solution :**

**Step 1 : **

Let M and D represent the set of Indian men and Doctors respectively.

**Step 2 : **

From the information given in the question, we have

n(M) = 23, n(D) = 4, n(MuD) = 24,

**Step 3 : **

From the basic stuff, we have

n(MuD) = n(M) + n(D) - n(MnD)

24 = 23 + 4 - n(MnD)

n(MnD) = 3

n(Indian Men and Doctors) = 3

**Step 4 : **

So, out of the **4** Indian doctors, there are **3** men.

And the remaining **1** is Indian women doctor.

**Hence, the number women doctors attending the conference is 1**

After having gone through the stuff given above, we hope that the students would have understood "Sets word problems worksheets".

Apart from the stuff given above, if you want to know more about "Sets word problems worksheets", please click here

Apart from the stuff, "Sets word problems worksheets", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**