Rose Harrison and Clara Huizink Solutions for Exercise 16: Practice 6

Of $150$ new university students, $85$ signed up for Mathematics and $70$ for Physics, while $50$ signed up for both subjects. By drawing a Venn diagram, determine how many students signed up for only Mathematics.

Of $150$ new university students, $85$ signed up for Mathematics and $70$ for Physics, while $50$ signed up for both subjects. By drawing a Venn diagram, determine how many students signed up for only Physics.

Of $150$ new university students, $85$ signed up for Mathematics and $70$ for Physics, while $50$ signed up for both subjects. By drawing a Venn diagram, determine how many students signed up for neither Mathematics nor Physics.

There are $30$ students involved in three different school clubs: chess, archery and cookery. Of these, $5$ students are in all three clubs, $6$ of them are only in the cookery club, $2$ are in chess and cookery but not archery, $15$ belong to cookery in total, $2$ are only in chess, and $3$ are only in archery. By drawing a Venn diagram, determine how many students are in the chess club.

There are $30$ students involved in three different school clubs:  chess, archery and cookery. Of these, $5$ students are in all three clubs, $6$ of them are only in the cookery club, 2 are in chess and cookery but not archery, $15$ belong to cookery in total, $2$ are only in chess, and $3$ are only in archery. By drawing a Venn diagram, determine ho many students are in:

the archery and cookery clubs only

In a class of $32$ students, $5$ live in the school town and travel to school by bus, and they have school lunches. $3$ live in the school town and travel to school by bus, but do not have school lunches. $9$ students do not live in the school town, do not travel by bus and do not have school lunches. $11$ students live in the school town and have school lunches. A total of $16$ students live in the school town. $9$students travel to school by bus and have school lunches. $13$ students travel to school by bus. By drawing a Venn diagram, determine how many students in total have school lunches.

The Venn diagrams below represent participants in an after school sports program. The students can choose to select table tennis(T), basketball(B), or squash (S). The given diagram represents $T\cap a\cap B$. Find $a$

The Venn diagrams below represent participants in an after school sports program. The students can choose to select table tennis(T), basketball(B), or squash (S). Given below diagram represents $a-\left(B \cup S\right)$. Find $a$.