Question

the venn diagram below shows the number of people in a room labeled with their like of cats and/or dogs. how many people are in the room? how many people like dogs but not cats? how many people like cats and dogs? how many people dont like dogs? how many people like dogs? how many people dont like cats? how many people like cats?

Explanation:

Step1: Find total number of people

Add all the non - overlapping and overlapping parts of the Venn diagram.
$19 + 12+18 + 5=54$

Step2: People who like dogs but not cats

This is the non - overlapping part of the dogs circle.
$18$

Step3: People who like cats and dogs

This is the overlapping part of the two circles.
$12$

Step4: People who don't like dogs

This is the non - dogs part which is the sum of the non - overlapping cats part and the part outside both circles.
$19 + 5=24$

Step5: People who like dogs

This is the sum of the non - overlapping dogs part and the overlapping part.
$18 + 12=30$

Step6: People who don't like cats

This is the non - cats part which is the sum of the non - overlapping dogs part and the part outside both circles.
$18+5 = 23$

Step7: People who like cats

This is the sum of the non - overlapping cats part and the overlapping part.
$19 + 12=31$

Answer:

How many people are in the room? 54
How many people like dogs but not cats? 18
How many people like cats and dogs? 12
How many people don't like dogs? 24
How many people like dogs? 30
How many people don't like cats? 23
How many people like cats? 31