Statement I: When methanol is added to water boiling point of water decreases.
Statement II: Methanol when added to water gives a non ideal solution with negative deviation.

CH₃OH-CH₃OH ....... Inter molecular H-bonding

H₂O-H₂O .......   Inter molecular H-bonding

H₂O-CH₃OH ....... Inter molecular H-bonding

Inter molecular H-bonding between CH₃OH - H₂O

is weaker than in CH₃OH-CH₃OH and  H₂O-H₂O

VP of CH₃OH - H₂O is higher than expected

This Azeotropic mix. shows positive deviation from Raoult's law

VP is higher than expected its BP will be lesser than expected

BP of CH₃OH - H₂O is lesser than that of  any one of its components.

It is a minimum boiling azeotrope

CH₃OH - H₂O mix. ---  VP,higher than expected from Raoult's law ---- positive deviation

              (II) is false

                            ----   BP lesser than that of pure CH₃OH & H₂O -----  minimum boiling azeotrope

                (I) is true