Final answer:
The statement that a racemic mixture, containing equal amounts of two enantiomers and being optically inactive, is true because the opposite rotations of light by the enantiomers cancel each other out.
Step-by-step explanation:
A racemic mixture is indeed a mixture of equal amounts of the two enantiomers of a given chiral molecule. Enantiomers are molecules that are mirror images of each other and cannot be superimposed upon one another. The statement that a racemic mixture is optically inactive is true. This occurs because the enantiomers have opposite effects on plane-polarized light: one enantiomer will rotate polarized light in a clockwise direction (dextrorotatory), while the other will rotate light by the same amount but in the anticlockwise direction (levorotatory). When present in equal amounts, these rotations cancel each other out, resulting in no net rotation of the plane of polarization and hence the mixture does not exhibit optical activity.