## PRACTICE QUESTIONS ON SET OPERATIONS ANSWERS

Practice questions on set operations answers :

Here we are going to see some practice questions and solution of set operations.

## Practice questions on set operations answers

Question 1 :

From the given Venn diagram find

(i) A (ii) B (iii) A U B (iv) A n B

Also verify that n(A U B) = n(A) + n(B) - n(A n B)

Solution :

The variables inside the circle A are known as elements of the set A.

A = { a, b, d, e, g, h }

The variables inside the circle B are known as elements of  the set B.

B = { b, c, e, f, i, j, h }

The variables inside the circles A and B are known as elements of the set AUB.

A U B = { a, b, c, d, e, f, g, h, i, j }

The variables in the common region of A and B are known as elements of A n B.

A n B = { b, e, h }

To verify the given statement, we have to find the cardinal number of each set.

n (A)  =  6

n (B)  =  7

n (A U B)  =  10

n (A n B)  =  3

n(A U B) = n(A) + n(B) - n(A n B)

10  =  6 + 7 - 3

10  =  13 - 3

10  =  10

Hence it is proved.

Question 2 :

If n(U) = 38, n(A) = 16, n (AnB) = 12, n(B') = 20 find n(AUB) .

Solution :

n (A U B) = n (A) + n (B) - n (A n B)

n (B) = n (U) - n (B')

n (B) = 38 - 20  ==> 18

n (A U B) = n (A) + n (B) - n (A n B)

n (A U B) = 16 + 18 - 12

=  34 - 12

=  22

Hence the value of n (A U B) is 22.

Question 3 :

From the given Venn diagram find

(i) A (ii) B (iii) A U B (iv) A n B

Also verify that n(A U B) = n(A) + n(B) - n(A n B)

Solution :

The numbers inside the circle A are known as elements of set A.

A = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A)  =  8

The numbers inside the circle B are known as elements of set B.

B = { 3, 6, 9 }

n (B) = 3

The numbers inside the circles A and B are known as elements of the set AUB.

A U B = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A U B) = 8

The numbers in common region of A and B is known as elements of A n B.

A n B = {3, 6, 9}

n (A n B) = 3

n(A U B) = n(A) + n(B) - n(A n B)

8 = 8 + 3 - 3

8 = 8

Hence it is proved.

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 4 :

From the venn diagram, write the elements of set A n B

Solution :

The variables in common region of A and B are known as elements of A n B.

A n B = { b, e, h }

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 5 :

If n(A) = 12, n(B) = 17 and n(A U B) = 21, find n(A n B)

Solution :

By using the formula,

n(A U B) = n (A) + n (B) - n (A n B)

we may find the value of n (A n B)

21  =  12 + 17 - n (A n B)

21  =  29 - n (A n B)

n (A n B)  =  29 - 21  ==>   8

Hence the value of n (A n B) is 8.

Question 6 :

From the venn diagram, write the elements of the following sets

(i)  A'   (ii)  B'   (iii)  (A n B)'   (iv)  (A U B)'

Solution :

(i) A'

A' =  { c, f, i ,j }

(ii) B'

B' =  { a, d, g }

(iii) (A n B)'

(A n B)'  =  { a, d, g, c, f, i, j }

(iv) (A U B)'

(A U B)'  =  {  }  (or) null set

Question 7 :

If n(U) = 43, n (A) =  26 find n (A')

Solution :

By using the formula,

n (A) + n (A')  =  n (U)

we may find the value of n (A')

26 + n (A') = 43

Subtract 26 on both sides

26 - 26 + n (A')  =  43 - 26

n (A')  =  17

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 8 :

If n (U) = 38, n (A) = 16, n (A n B) = 12, n (B') = 20, find n (A U B).

Solution :

By using the formula,

n (B) + n (B')  =  n (U)

we may find the value of n (B')

n (B) + 20 = 38

Subtract 20 on both sides

n (B) + 20 - 20  =  38 - 20

n (B)  =  18

n (A U B) = n (A) + n (B) - n (A n B)

= 16 + 18 - 12

=  34 - 12

=  22

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 9 :

If A = {- 2, - 1,0,3,4}, B = {- 1,3,5}, find (i) A - B (ii) B - A

Solution :

A = {- 2, - 1,0,3,4} and B = {- 1,3,5}

A - B = { -2, 0, 4}

B - A = { 5 }

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 10 :

If A = {2, 3, 5, 7, 11} and B = {5, 7, 9, 11, 13} , find A Δ B.

Solution :

A = {2, 3, 5, 7, 11} and B = {5, 7, 9, 11, 13}

A - B = { 2, 3 }

B - A = { 9, 13 }

Δ B = (A - B) U (B - A)

=  { 2, 3, 9, 13 }

Let us see the answer for next problem on "Practice questions on set operations answers".

Question 11 :

Given that U = {3, 7, 9, 11, 15, 17, 18}, M = {3, 7, 9, 11} and N = {7, 11, 15, 17},

find (i) M - N    (ii) N - M     (iii) N' - M     (iv) M' - N

(v) M n (M - N)    (vi) N U (N - M)     (vii) n(M - N)

Solution :

U = { 3, 7, 9, 11, 15, 17, 18 }

M = { 3, 7, 9, 11 }

N = { 7, 11, 15, 17 }

(i) M - N

The set M - N would contain the elements of the set M excluding the elements of M n N

M - N = { 3, 9 }

(ii) N - M

The set N - M would contain the elements of the set M excluding the elements of N n M

N - M = { 15, 17 }

(iii) N' - M

N' = { 3, 9, 18 }

N' - M  =  {18}

(iv) M' - N

M' = { 15, 17, 18 }

M' - N = { 18 }

(v) M n (M - N)

The set M n (M - N) would contain the set of common elements that we found in both the set M and (M - N)

M = { 3, 7, 9, 11 }  M - N = { 3, 9 }

M n (M - N)  =  { 3, 9}

(vi) N U (N - M)

N = { 7, 11, 15, 17 }    N - M = { 15, 17 }

N U (N - M)  =  {  7, 11, 15, 17 }

(vii) n(M - N)

Number of elements of set M - N is 2.

Hence  n(M - N) =  2

## Related topics

After having gone through the stuff given above, we hope that the students would have understood "Practice questions on set operations answers".

Apart from the stuff given above, if you want to know more about "Practice questions on set operations answers", please click here

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

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