1060. Among natural numbers from 1 to 10000, which are there more of: those divisible by 7 but not by 11, or those divisible by 11 but not by 7?
$\triangle$ First, let's calculate the number of natural numbers from 1 to 10000 that are divisible by 7, as well as the number of natural numbers within the same range that are divisible by 11. The first set forms the sequence

$$
7 ; \quad 14=7 \cdot 2 ; \quad 21=7 \cdot 3 ; \quad \ldots ; \quad 7 \cdot 1428
$$

(1428 is the quotient from dividing 10000 by 7 with a remainder), so the number of such numbers is 1428. The second set forms the sequence

$$
11 ; \quad 22=11 \cdot 2 ; \quad 33=11 \cdot 3 ; \ldots ; 9999=11 \cdot 909
$$

so, the number of such numbers is 909.

There are more numbers that are divisible by 7.

If we now subtract from both sets those numbers that are divisible by both 7 and 11, the number of the first set, i.e., those that are divisible by 7 but not by 11, will still be greater.

Answer: there are more numbers that are divisible by 7 but not by 11.