Diholosides are condensates of two cyclic holosides:
α-D-Glucose(1→4)α-D-Glucose
Is reducing because a reopening of the cycle is possible in right position 1 to restore a reducing aldehyde function!
β-D-Glucose(1→4)β-D-Glucose
Is reducing because a reopening of the cycle is possible in right position 1 to restore a reducing aldehyde function!
β-D-Galactose(1→4)α-D-Glucose
Is reducing because a reopening of the cycle is possible in right position 1 to restore a reducing aldehyde function!
α-D-Glucose(1→2)β-D-Fructose
It is not reducing, because the 1→2 bond blocks the two possible carbonyl positions!