From the truth table of $A\rightarrow B$, we know that $True\rightarrow False=False$, and rest all are $True$.
Take $P=True$, and $Q=False$.
Then $(True\rightarrow False)\wedge(False \rightarrow True)=False\wedge True=False.$ This proves it is not a tautology.
Take $P=Q=True.$
Then$(True\rightarrow True)\wedge(True\rightarrow True)=True\wedge True=True.$ This proves it is not a contradiction either, and since it is taking up values depending on the variables, it is a contingency.