Question

a survey was conducted to see if people like marvel comics and whether they like dc comics. of the 100 people surveyed, 70 like marvel, 82 like dc comics, and 65 like both.
a) ( a=), ( b=), ( c=), ( d=)
b) how many people liked marvel, and not dc?
c) how many people surveyed do not like either?

Explanation:

Step1: Calculate \( A\)

\( A=\text{Number of people who like Marvel only}=\text{Total who like Marvel}-\text{Those who like both}\)
\( A = 70 - 65=5\)

Step2: Calculate \( C\)

\( C=\text{Number of people who like DC only}=\text{Total who like DC}-\text{Those who like both}\)
\( C = 82 - 65 = 17\)

Step3: Calculate \( D\)

\( D=\text{Number of people who like neither}=\text{Total surveyed}-(A + B + C)\)
\( A + B + C=5 + 65+17 = 87\)
\( D=100 - 87 = 13\)

For part b), the number of people who liked Marvel and not DC is \( A = 5\). For part c), the number of people who do not like either is \( D = 13\)

Answer:

a) \( A = 5\), \( B = 65\), \( C = 17\), \( D = 13\)
b) \( 5\)
c) \( 13\)