Logic level and switch direction in relation to circuit

I am new to logic design and circuity. I saw two diagrams from a learning resource that are circuits will supposed operate an LED light as shown below:

Diagram A:

Diagram B:

Based upon these two diagrams I am trying to understand the logic level for each must be to turn on the LED light, and which switch must be closed to turn on the light.

From my understanding, a HIGH logic level corresponds to a binary 1 meaning on, and a LOW logic level corresponds to a binary 0 meaning off. I thought that diagram A's logic level to turn on the light would be 1 since I thought the circuit is in 0 position currently; that the diagram A's S1 switch must be turned on to turn on the light; that the diagram B's logic level to turn on the light would be 0 since I thought the circuit is in 1 position currently; that the diagram B's S1 switch must be turned on to turn on the light.

After much research, I am still not understanding the logic levels these two diagrams should be predicting, and the switch that should be closed to turn on the LED light. Please excuse my elementary understanding of circuity as it is one of my first times encountering a circuit diagram, and I am trying to learn off ones like these.

A closed circuit is the one which goes from positive of the battery to negative of the battery and completes the circuit.

With this basic rule, Switch S1 in diagram A and switch S2 in diagram B should be turned on to power the LED.