Q1. A survey of the UPI students who read 3 newspapers found that 96 students read Imvaho, 52 students read new times, 72 students read Daily times, 16 read new times and Imvaho, 10 read New Times and Daily times, 8 read Imvaho and Daily times and 9 read none of 3 newspapers. If 200 students were asked, then: Draw the Venn-diagram to illustrate the above situation. /4Marks Find the number of students who read 3 newspapers /2Marks Find the number of students who read new times and Imvaho only /2Marks Find the number of students who read only Daily times /2Marks

The formula is: |I ∪ N ∪ D| = |I| + |N| + |D| - |I ∩ N| - |I ∩ D| - |N ∩ D| + |I ∩ N ∩ D| Substitute the known values:
191 = 96 + 52 + 72 - 16 - 8 - 10 + |I ∩ N ∩ D|
191 = 220 - 34 + |I ∩ N ∩ D|
191 = 186 + |I ∩ N ∩ D| |I ∩ N ∩ D| = 191 - 186 |I ∩ N ∩ D| = 5

The number of students who read 3 newspapers is 5.

This is the intersection of N and I, excluding those who also read D.
Number of students who read N and I only = |I ∩ N| - |I ∩ N ∩ D|
= 16 - 5
= 11

The number of students who read New Times and Imvaho only is 11.

First, find the number of students who read Daily Times and Imvaho only, and Daily Times and New Times only. |I ∩ D only| = |I ∩ D| - |I ∩ N ∩ D| = 8 - 5 = 3 |N ∩ D only| = |N ∩ D| - |I ∩ N ∩ D| = 10 - 5 = 5

Now, calculate those who read only Daily Times: |D only| = |D| - (|I ∩ D only| + |N ∩ D only| + |I ∩ N ∩ D|) = 72 - (3 + 5 + 5)
= 72 - 13
= 59

The number of students who read only Daily Times is 59.

Let x = |I ∩ N ∩ D| = 5.

• Students who read only Imvaho: |I only| = |I| - (|I ∩ N only| + |I ∩ D only| + x) = 96 - (11 + 3 + 5) = 96 - 19 = 77

• Students who read only New Times: |N only| = |N| - (|I ∩ N only| + |N ∩ D only| + x) = 52 - (11 + 5 + 5) = 52 - 21 = 31

• Students who read only Daily Times: |D only| = 59 (calculated in Step 4)

• Students who read Imvaho and New Times only: |I ∩ N only| = 16 - 5 = 11

• Students who read New Times and Daily Times only: |N ∩ D only| = 10 - 5 = 5

• Students who read Imvaho and Daily Times only: |I ∩ D only| = 8 - 5 = 3

• Students who read all three newspapers: |I ∩ N ∩ D| = 5

• Students who read none of the three newspapers: None = 9

To illustrate the Venn diagram, you would draw three overlapping circles (I, N, D).

• The central region (I ∩ N ∩ D) would contain 5.
• The region for I ∩ N only would contain 11.
• The region for N ∩ D only would contain 5.
• The region for I ∩ D only would contain 3.
• The region for I only would contain 77.
• The region for N only would contain 31.
• The region for D only would contain 59.
• The region outside all circles would contain 9.