According to the title description, the third line of your truth table, the result of P=F and Q=T, should be FALSE. After correcting the truth table, it is easily seen to be a description of a 2-input Exclusive-NOR gate. **broken link removed**
1) Result=not(p) or (P and Q)
2) Distribute not(p): result=(not(p) or p) and (not(p) or q)
3) Use identities: result=1 and (not(p) or q)
4) Simplify: result= not(p) or q.