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In order to identify boolean queries that are not valid and do not have parentheses, you need to follow the operator precedence for boolean operators.
The precedence order is: 1. NOT 2. AND 3. OR
If there are multiple operators without parentheses, then the operators with higher precedence will be applied first. So if you see an invalid query without parentheses and multiple operators, examine it using this order of precedence to see if it can be made valid.
For example, consider the query "blue AND red OR" - this is invalid and doesn't make sense. But if we rearrange it as "(blue AND red) OR" or "blue AND (red OR)", it becomes a valid query.
Similarly, for the query "NOT AND blue OR red", we can rearrange it as "NOT (AND blue) OR red" or "NOT AND (blue OR red)" to make it valid.
In general, the best way to avoid confusion is to always use parentheses to clearly define the order of operations in a boolean query.