Remove value from bitwise or-combined integer?

Question

Using the Bitwise Or operator you can combine integers, for example integers that are powers of 2, with each other, and later check if the returned int contains a specified value. But is there a proper way to remove values from the returned integer without combining a new one?

Currently I subtract the value that I want to remove from the combined integer, but does this work fine or can it cause issues? Or is there any more "proper" way of doing it?

Here's my code:

private void button1_Click(object sender, EventArgs e)
{
    int combinedints = CombineIntegers(CombineIntegers(2, 8), 32); //Combine three integers.
    MessageBox.Show(combinedints.ToString()); //Shows 42.
    MessageBox.Show(RemoveInteger(combinedints, 8).ToString()); //Removes 8 - shows 34.
}

private int CombineIntegers(int a, int b)
{
    return a | b;
}

private int RemoveInteger(int a, int b)
{
    return a -= b;
}

private bool CheckInteger(int a, int b)
{
    return (a & b) == b;
}

Answer 1

private int RemoveInteger(int a, int b)
{
    return a & ~b;
}