conclusion

signals

Lactose absent
Lactose present, glucose present
Lactose present, glucose absent
Lactose absent, glucose absent

Lactose absent Lac Operon State

OFF

Lactose absent Reason

LacI binds operator; no allolactose to remove it

Lactose present, glucose present Lac Operon State

LOW (basal)

Lactose present, glucose present Reason

CRP-cAMP inactive (low cAMP); LacY blocked by inducer exclusion

Lactose present, glucose absent Lac Operon State

HIGH (fully ON)

Lactose present, glucose absent Reason

LacI released by allolactose; CRP-cAMP activates transcription

Lactose absent, glucose absent Lac Operon State

OFF (or very low)

Lactose absent, glucose absent Reason

No allolactose → LacI remains bound; CRP-cAMP present but repressor is activ