A reactive element , in an AC circuit causes the current flowing.

1. To lead by pi by two

2. to lag in phase by pi by two w.r.t. the applied voltage

Identify the element in each case.

1. In case of pure capacitive circuit, the current leads in phase by pi/2 with respect to the applied voltage. So, the element will be a capacitor.
2. In case of pure inductive circuit, the current lags in phase by pi/2 with respect to the applied voltage. So, the element will be an inductor.