Que 3 MATHS practise asssigment week 1 , solution mistake

[patildhairya...@gmail.com]

in que 3, u have mentioned set C as( 2,4,5,...50) whereas in next que 4 u have included {1,100} in same set B which is of  set of all natural numbers which divide 100

WHICH ONE TO CONSIDER ???????   QUE 3 OR 4 >>>>>>>>>

reference 

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3. Let A be the set of all even natural numbers (including zero), B be the set of all odd natural

numbers, C be the set of all natural numbers which divide 100, and D be the set of all

prime numbers less than 100. Which of the following is(are) correct representation of these

sets? [Note: A region represented in a Venn diagram could be empty. Take the set of real

numbers to be the universal set.]

By definition, A = {0, 2, 4, 6, 8,. . . }, B = {1, 3, 5, 7,. . . }, C = {2, 4, 5, 10,. . . ,

50} and D = {2, 3, 5, 7, 11,.., 97}.

Option 1 shows D as a subset of all odd natural numbers. But D contains element 2,

whereas B does not. Hence, this option is wrong.

Option 2 has overlap between A and C and overlap between B and C, but no overlap

between A and B. A and B are sets of even and odd natural numbers which have no

overlap. C is the set of natural numbers which divide 100. A ∩ C = {2, 4, 10, 20, 50} and

B ∩ C = {1, 5, 25}. Hence, this option is correct.

Option 3 represents C and D sets with an overlap between them. The overlapping area

includes the set of all prime numbers which can divide 100. This is the set {2, 5}. Hence,

option 3 is also correct.

A ∩ D = {2}, but there is no overlap between A and D in Option 4. Hence, this option is

wrong.

Page 4

4. Let A be the set of natural numbers which are multiples of 5 strictly less than 100, and B

be the set of natural numbers which divide 100. What are the cardinalities of the following

sets?

B \ A (the set of elements in B but not in A), A ∩ B, and B

(2, 5, 7)

(4, 5, 9)

(3, 4 , 7)

(3, 5, 8)

Solution: By definition, A = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80,

85, 90, 95}, B = {1, 2, 4, 5, 10, 20, 25, 50, 100}, B \A = {1, 2, 4, 100} and A∩B = {5, 10,

20, 25, 50}. It follows that the cardinalities of sets B \ A, A ∩ B and B are, respectively,

4, 5 and 9. Hence, option 2 is correct.

[Venkatesan Shesha Srikanth]

Hi,

     The set of all natural numbers that divides 100 is {1,2,4,5,10,20,25,50,100} and cardinality of this set is 9. Thanks for pointing out the mistake, we will rectify it !!

Regards

srikanth venkatesan