According to the definitions of national saving and public saving, if Y, C, and G remained the same, an increase in taxes would

An increase in tax would leave national saving unchanged and raise public saving.

Explanation:

If we recall both the definition of national saving saving and public savings, we have,

National Saving: The total sum of money saved by the government with the total sum saved by the private sector. It should be noted that this is excluding of government spending.

Public Savings: This can be categorized as revenue or savings raised by the government through tax and other sectors under the government control. This also exclude government spending.

So referring back to the question, an increase in tax will make national saving the same and will increase public savings.