Help building a latch from 1 AND gate and 1 OR gate
Use a 2-input OR gate and wire the output to input B. Providing the A input is low, the OR gate output stays low until the A input rises due to an alarm trigger. This forces the OR gate output high and this will stay high until power is removed.

A variation of this is to gate the feedback to the OR gate's B input via an AND gate. The other input on the AND gate controls whether the OR gate can latch or not: -