Test Question

Question 1

In a survey of 300 people, it was found that 150 people liked I-phone and 200 people like Android phone. But 25 people did not like any of these two phones.

1. If I and A denote the sets of people who like I-phone and Android phone respectively, write the cardinality of \(n (\overline{I \cup A})\). [1]
2. Present the above information in a Venn-diagram. [1]
3. Find the number of people who liked I-phone only. [3]
4. Compare the number of people who like both I-phone and Android phone and who do not like any of these two phones. [1]

Section 1: Given

1. 300 represents for n(U) n(A) n(B) n(A∪B) n(A∩B) n(A') n(B') n(A-B) n(B-A) n(A∪B)' n(A∩B)' n(A∆B) n(A∆B)' n(A-B)' n(B-A)'


2. 150 represents for n(U) n(A) n(B) n(A∪B) n(A∩B) n(A') n(B') n(A-B) n(B-A) n(A∪B)' n(A∩B)' n(A∆B) n(A∆B)' n(A-B)' n(B-A)'


3. 200 represents for n(U) n(A) n(B) n(A∪B) n(A∩B) n(A') n(B') n(A-B) n(B-A) n(A∪B)' n(A∩B)' n(A∆B) n(A∆B)' n(A-B)' n(B-A)'


4. 25 represents for n(U) n(A) n(B) n(A∪B) n(A∩B) n(A') n(B') n(A-B) n(B-A) n(A∪B)' n(A∩B)' n(A∆B) n(A∆B)' n(A-B)' n(B-A)'

Section 2: To Find

1. Write the cardinality of \( n(\overline{I \cup A}) \):


2. Select the correct Venn diagram:
   OPT1

   OPT2

   OPT3

   OPT4

   OPT5


3. Find the number of people who liked iPhone only:


4. Compare the number of people who like both iPhone and Android and who do not like any of these two phones: -- Select comparison -- people who like both is 3 times of people who like none people who like both 50 more than people who like none people who like none is 50 less than people who like both

Full Score: [8]

1. The cardinality of people who like none of the phones is
   \(n (\overline{I \cup A}) = 25\)
2. Venn-diagram representation
3. To find I-phone only
   From Venn-diagram, we see that
   (150-x) + x + (200-x) + 25 = 300
   or375 - x = 300
   orx = 75
   Thus
   The number of people who liked I-phone only is = 150 - 75 = 75.
4. The number of people who like both (75) is three times the number of people who like none (25).