Question

In a survey of 548 students, 162 read the Guardian and 124 read The Vanguard. 320 Students read neither. Illustrate these facts in a Venn diagram . How many students read neither the Guardian or the Vanguard

Answer 1

In the survey of 548 students, a Venn diagram would show 104 students exclusively read the Guardian, 66 students exclusively read The Vanguard, 58 students read both, and 320 students read neither.

Step-by-step explanation:

To illustrate the facts given in the survey of 548 students in a Venn diagram, we need to identify the groups and the relationships between them.

Let's denote one circle as students who read the Guardian (G), and the other as students who read The Vanguard (V). The students who read both newspapers will fall into the intersection of the two circles.

According to the inclusion-exclusion principle, we can calculate the number of students who read both newspapers by adding the totals of each paper's readers and subtracting the number of students who read neither:

Students who read the Guardian or The Vanguard = Total students - Students who read neither
= 548 - 320
= 228 students
Students who read both the Guardian and The Vanguard = (Students who read the Guardian) + (Students who read The Vanguard) - Students who read the Guardian or The Vanguard
= 162 + 124 - 228
= 58 students

The Venn diagram would then show:

• 104 students only read the Guardian (162 total - 58 who read both)
• 66 students only read The Vanguard (124 total - 58 who read both)
• 58 students read both the Guardian and The Vanguard
• 320 students read neither

In conclusion, 58 students read both the Guardian and The Vanguard, and 320 students read neither.