- $M=\{\text{members}\}$
- $m=|M|=25$ (given)
- $M_t=\{\text{members playing tennis}\}$
- $m_t=|M_t|=10$ (given)
- $M_s=\{\text{members playing squash}\}$
- $m_s=|M_s|=12$ (given)
- $M_{ts}=\{\text{members playing tennis and squash}\}$
- $m_{ts}=|M_{ts}|=3$ (given)
- $M^*_t=\{\text{members playing tennis only}\}=M_t\setminus M_{ts}$
- $m^*_t=|M^*_t|=|M_t|-|M_{ts}|=m_t-m_{ts}=10-3=7$.
- $M^*_s=\{\text{members playing squash only}\}=M_s\setminus M_{ts}$
- $m^*_s=|M^*_s|=|M_s|-|M_{ts}|=m_s-m_{ts}=12-3=9$.
- $M_t\cup M_s=\{\text{members playing some sport}\}=M_t^*\amalg M_s^*\amalg M_{ts}$
- $|M_t\cup M_s|=m^*_t+m^*_s+m_{ts}=(m_t-m_{ts})+(m_s-m_{ts})+m_{ts}$
$=m_t+m_s-m_{ts}=10+12-3=19$ - $M^*=\{\text{members playing no sport}\}=M\setminus(M_t\cup M_s)$
- $m^*=|M^*|=|M|-|M_t\cup M_s|=m-(m_t+m_s-m_{ts})$
$=m-m_t-m_s+m_{ts}=25-10-12+3=6$