(a) Under parity, a "true" scalar operator does not change:
Π^†f^Π^=f^,
whereas a pseudoscalar changes sign. Show therefore that [Π^,f^]=0 for a "true" scalar, whereas {Π^,f^}=0 for a pseudoscalar. Note: the anti-commutator of two operators A^ and B^ is defined as {A^,B^}≡A^B^+B^A^.
(b) Similarly, a "true" vector changes sign
Π^†V^Π^=−V^,
whereas a pseudovector is unchanged. Show therefore that {Π^,V^}=0 for a "true" vector and [Π^,V^]=0 for a pseudovector.