The problem given to me is :In a certain discrete math class, three quizzes (each marked out of $15$) were
given. Out of the $35$ students in the class:
$15$ students scored $12$ or above on quiz #$1$,
$12$ students scored $12$ or above on quiz #$2$,
$18$ students scored $12$ or above on quiz #$3$,
$7$ students scored $12$ or above on quizzes #$1$ and #$2$,
$11$ students scored $12$ or above on quizzes #$1$ and #$3$,
$8$ students scored $12$ or above on quizzes #$2$ and #$3$,
$4$ students scored $12$ or above on quizzes #$1$, #$2$ and #$3$.
I know that the number of students that scored $12$ or above on at least one quiz is $23$. Since $N(1\cup2\cup3) = 15+18+12-7-11-8+4= 23$.
How do I get the students that got $12$ or above in quiz $1$ and $2$ but not in $3?$ Do I subtract $18$ by $23?$
Construct a Venn diagram by working through the statements in reverse order. You should get the following diagram which will let you answer the question.