Equivalence relations

1. Show that $\dashv$ $\vdash$ (introduced in §5.1) is an equivalence relation;
2. Show that if P $\dashv$ $\vdash$ Q and R $\dashv$ $\vdash$ S, then:
   1. $\neg$P $\dashv$ $\vdash$ Q;
   2. [P $\vee$ R] $\dashv$ $\vdash$ [Q $\vee$ S];
   3. [P $\leftrightarrow$ R] $\dashv$ $\vdash$ [Q $\leftrightarrow$ S].

Readings

(Hodges, 2001, §§30-33)

Sainsbury (2001)