Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to ______.

We need to count 4-digit numbers $$\leq 2800$$ divisible by 3 or by 11.

4-digit numbers range from 1000 to 2800.

Using inclusion-exclusion: $$|A \cup B| = |A| + |B| - |A \cap B|$$

Divisible by 3 (set A):

From 1000 to 2800: First multiple of 3 $$\geq 1000$$ is 1002. Last $$\leq 2800$$ is 2799.

Count = $$\frac{2799 - 1002}{3} + 1 = \frac{1797}{3} + 1 = 599 + 1 = 600$$

Divisible by 11 (set B):

First multiple of 11 $$\geq 1000$$: $$\lceil 1000/11 \rceil = 91$$, so $$91 \times 11 = 1001$$.

Last $$\leq 2800$$: $$\lfloor 2800/11 \rfloor = 254$$, so $$254 \times 11 = 2794$$.

Count = $$254 - 91 + 1 = 164$$

Divisible by 33 (set A ∩ B):

First $$\geq 1000$$: $$\lceil 1000/33 \rceil = 31$$, so $$31 \times 33 = 1023$$.

Last $$\leq 2800$$: $$\lfloor 2800/33 \rfloor = 84$$, so $$84 \times 33 = 2772$$.

Count = $$84 - 31 + 1 = 54$$

Result:

$$|A \cup B| = 600 + 164 - 54 = 710$$

The answer is $$\boxed{710}$$.