How do we decide which circuit is a latch?

Question

1. Will A and B always be the complement of one another regardless of what logic gates we use in the latch-like circuit? For instance (the two circuits shown as examples):

2. How do we decide whether A and B will be the complement of one another or not?

3. How to find the invalid states?

4. Are these two latches?

^{simulate this circuit – Schematic created using CircuitLab}

OR

^{simulate this circuit}

I have tried following a few videos for instance this. But the presenter says that a certain state is invalid because Q and Q' should be the complement of each other. But how do we decide/prove that Q and Q' are the complement of one another?

UPDATE:

Truth Table of First Circuit:

How do I derive answers to the above questions from here.

Answer 1

To have a valid latch there must be three distinct values of the inputs:

1. One set of input values that forces the latch to a logic 1 state

2. One set of input values that forces the latch to a logic 0 state

3. One set of input values that holds the current state, whether it is 0 or 1

A valid latch circuit must also have an output signal, typically called Q, that reflects the stored state of the latch.

Set up the truth tables for each circuit and see if you can find the necessary input conditions for the circuit to be a latch.