For two sets A and B, what is n(A\capB) ? I. n(A)=6 and n(B-A)=8 II. n(A-B)=8=n(B-A) and {n}({A}\cup{B})=24

Correct Answer is : if the statement II alone is sufficient to answer the question.

if the statement I alone is sufficient to answer the question.

if the statement II alone is sufficient to answer the question.

if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.

if both the statements I and II together are not sufficient to answer the question and additional data is required.

AP ICET 2015 Paper

Question : 20 of 200

Marks: +1, -0

For two sets A and B, what is

n(A∩B)

?
I.

n(A)=6

and

n(B-A)=8

II.

n(A-B)=8=n(B-A)

and

{n}({A}∪{B})=24

if the statement I alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

We have,

n(A∩B)=n(A∪B)-n(A–B)–n(B–A)

I. Given

n(A)=6,n(B–A)=8

Since n(B) or n(A – B)are not given, I alone is not sufficient
II. Given:

n(A-B)=8,n(B-A)=8,n(AB)=24

n(A∩B)=24-8-8=8

∴ II alone is sufficient.

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