UPSC NDA 2 2019 Mathematics Solved Paper

Concept:
If A,B and C are subsets of a set X . Then
I. A∪(B∩C)=(A∪B)∩(A∪C)
II. A∪A=A,A∩(A∪B)=A,A∪(A∩B)=A and A∩A=A
III. (A∩B)∪C=(A∩C)∪(B∩C)
IV. (A∪B)∩C=(A∩C)∪(B∩C)
Calculation:
⇒A∪(A∩B)=(A∪A)∩(A∪B)=A∩(A∪B)=A‌‌−( Using property I and II)
So, option 1 is not correct.
⇒A∩(A∪B)=(A∩A)∪(A∩B)=A∪(A∩B)=A‌‌−(U sing property I and II)
So, option 2 is correct.
⇒(A∩B)∪C=(A∪C)∩(B∪C)‌‌−( Using property III)
So, option 3 is correct.
⇒(A∪B)∩C=(A∩C)∪(B∩C)‌‌−( Using property IV)
So, option 4 is correct.