-
$m=40$,
$m_t=10$,
$m_s=15$,
$m_b=12$,
$m_{ts}=5$,
$m_{tb}=4$,
$m_{sb}=3$,
$m_{tsb}=2$.
- $m_{ts}^*=\text{number playing tennis and squash only}$
$m_{ts}^*=m_{ts}-m_{tsb}=5-2=3$
- $m_{tb}^*=m_{tb}-m_{tsb}=4-2=2$;
$m_{sb}^*=m_{sb}-m_{tsb}=3-2=1$.
- $m_t^*=\text{number playing tennis only}$
$m_t^*=m_t-(m^*_{ts}+m^*_{tb}+m_{tsb})
= m_t-m_{ts}-m_{tb}+m_{tsb}$
$=10-5-4+2=3$
- $m_s^*=m_s-m_{ts}-m_{sb}+m_{tsb}=15-5-3+2=9$
- $m_b^*=m_b-m_{tb}-m_{sb}+m_{tsb}=12-4-3+2=7$
- $m'=\text{number playing some sport}$
$m'=m_t^*+m_s^*+m_b^*+m_{ts}^*+m_{tb}^*+m_{sb}^*+m_{tsb}=27$
- $m^*=\text{number playing no sport}$
$m^*=m-m_t^*-m_s^*-m_b^*-m_{ts}^*-m_{tb}^*-m_{sb}^*-m_{tsb}=13$
$m^*=m-m_t-m_s-m_b+m_{ts}+m_{tb}+m_{sb}-m_{tsb}=13$
- $\text{number playing tennis or squash}=m_t+m_s-m_{ts}=20$
- $\text{number playing tennis or badminton}=m_t+m_b-m_{tb}=18$
- $\text{number playing squash or badminton}=m_s+m_b-m_{sb}=24$