Rose Harrison and Clara Huizink Solutions for Exercise 20: Mixed practice

Determine whether the following statement is true or false. If false, explain why.

$\left\{\text{ primes }\right\}\subseteq \left\{\text{ odd integers }\right\}$

Determine whether the following statement is true or false. If false, explain why.

$\text{ If }U=\mathrm{\mathbb{N}},\text{ then }{\left({\mathrm{\mathbb{Z}}}^{+}\cap \mathrm{\mathbb{N}}\right)}^{\text{'}}=\left\{0\right\}$

Determine whether the following statement is true or false. If false, explain why.

$2\subseteq \left\{\text{ primes }\right\}$

In a school sports day, medals were awarded as follows: $36$ in running, $12$ in high jump, and $18$ in discus. The medals were awarded to a total of $45$ students, and only $4$ students received medals in all three events. Determine how many students received medals in exactly two out of three events.

A survey of $39$ university students found:
$10$ worked part-time while studying
$18$ received financial help from home
$19$ withdrew money from their savings as needed
$2$ financed themselves from all three sources
$12$ received financial help from home only
$5$ received financial help from home and withdrew money from savings
$6$ financed themselves only by working part-time and withdrawing money from savings.

Determine how many students did not finance themselves using any of the three resources.

A survey of $39$ university students found:
$10$ worked part-time while studying
$18$ received financial help from home
$19$ withdrew money from their savings as needed
$2$ financed themselves from all three sources
$12$ received financial help from home only
$5$ received financial help from home and withdrew money from savings
$6$ financed themselves only by working part-time and withdrawing money from savings.

Determine how many students worked part-time and received money from home.

A survey of $39$ university students found:
$10$ worked part-time while studying
$18$ received financial help from home
$19$ withdrew money from their savings as needed
$2$ financed themselves from all three sources
$12$ received financial help from home only
$5$ received financial help from home and withdrew money from savings
$6$ financed themselves only by working part-time and withdrawing money from savings.

Determine how many students received financial help from home and withdrew money from their savings.

A survey of $39$ university students found:
$10$ worked part-time while studying
$18$ received financial help from home
$19$ withdrew money from their savings as needed
$2$ financed themselves from all three sources
$12$ received financial help from home only
$5$ received financial help from home and withdrew money from savings
$6$ financed themselves only by working part-time and withdrawing money from savings.

Determine how many students financed themselves using only one of the three ways surveyed.