mock test question 4

[Kalyani Manoj]

  Let S1 be the set of irrational numbers between 0 and 1, S2 be the set of rational numbers between 0 and 1 (including both 0 and 1), and S be the closed interval [0, 1]. Which of the following options are correct? (MSQ) [3]

 S1 ∩ S2 is an empty set.

 S1 ∪ S2 = S

 S1 ∪ S2 is a proper subset of S.

 S2 is a finite set. 

 S \ S2 = S1

a. can you please tell me how is S \ S2 = S1... (isnt s1+s2=s)how is this way possible... can you please explain...

b. S1 ∪ S2 is a proper subset of S... can you please tell why this is false??why is it not a proper subset of s?

[soniya duge]

S \ S2 = S1 this means remove element present in S2 set from S set. So the remaining set is equal to S1. Hence it is true.

b. S1 ∪ S2 is a proper subset of S... can you please tell why this is false??why is it not a proper subset of s? 

S1 u S2 = S hence it is not a proper subset. To be a proper subset, at least one element of S should not be an element of S1 U S2

example:- 

A = {1,2,3,4,5}

B = {2,3,4,5}

Here you may say that B is proper subset of A.

But if B = {1,2,3,4,5} then this is not call a proper subset.

Hope this clears your doubt.

Regards,

Soniya Duge