Question

In a class of 28 students everyone like math, english, or both. if 17 like math and 19 like english how many like both?

A) 2
B) 8
C) 16
D) 20
E) 28

Answer 1

Maths be A and English be B

• A+B-A
  `\cap` B=AUB

A intersection B be X

• (A-X)+(B-X)+X=AUB
• A+B-X=28
• 17+18-X=18
• 35-X=28
• X=8

Option B

Answer 2

• B) 8 students like both

===========================

Let the numbers be:

• M - likes math, M = 17;
• E - likes English, E = 19;
• B - likes both, B is unknown;
• T- total number, T = 28.

Since both M and E include B, we can show the total as:

• Math only + English only + Both = Total

and

• Math only = M - B
• English only = E - B

The total can be expressed as:

• M - B + E - B + B = T
• M + E - B = T

Substitute values and solve for B:

• 17 + 19 - B = 28
• 36 - B = 28
• B = 36 - 28
• B = 8

This is matching the answer choice B)