SOLVING WORD PROBLEMS INVOLVING SETS

Problem 1 :

There are 40 students in a class. 20 take Chemistry and 25 take French. 8 students take both.

(i)  Find how many students take none.

(ii)  How many are there in at least one classes?

Solution :

Total number of students  =  40

Let A and B be the students who took Chemistry and French respectively.

n(A)  =  20, n(B)  =  25 and n(AnB)  =  8

n(AUB)  =  n(A) + n(B) - n(AnB)

n(AUB)  =  20 + 25 - 8

  =  45 - 8

n(AUB)  =  37

Number of students who take none  =  Total number of students - Number of students who take one

=  40 - 37

=  3

So, the number of students who take none is 3 and number of students are in atleast one class is 37.

Problem 2 :

A group of 20 college students were asked whether they are using the social net working sites. For that 8 said they use face book. 10 said they use twitter. 4 said they use both.

(i)  Find how many are not using none?

(ii)  Find how many are using only face book and twitter?

Solution :

Let A and B be the students who uses Face book and twitter respectively.

Number of students  =  20

n(A)  =  8, n(B)  =  10, n(A n B)  =  4

(i)  To find the number of students who are not using any of these, we have to subtract number of students who uses one from the total number of students.

n(A U B)  =  n(A) + n(B) - n(A n B)

  =  8 + 10 - 4

  =  14

Number of students who use none  =  20 - 14

  =  6

Number of students who use face book  =  n(A) - n(A n B)

  =  8 - 4

  =  4

Number of students who use twitter  =  n(B) - n(A n B)

  =  10 - 4

  =  6

Problem 3 :

At a breakfast buffet, 20 people chose coffee and 17 chose juice. 10 people chose both coffee and juice. If each person chose at least one of these beverages, how many people visited the buffet?

Solution :

Let A and B be the students who choose coffee and juice respectively.

n(A)  =  20, n(B)  =  17, n(AnB)  =  10

n(AUB)  =  n(A) + n(B) - n(AnB)

n(AUB)  =  20 + 17 - 10

  =  37 - 10

n(AUB)  =  27

So, the number of people who visited the buffet is 27.

Apart from the stuff given in this section,  if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

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

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6