Is zero an element of all integers?
Yes.....0 is an element of all integers Integers can be thought of as points on an infinitely long number line
The sign of the product of four integers depends on the signs of the individual integers. There are 4 cases: 1) When all 4 integers share the same sign and all are non-zero (either all are positive or all are negative), the product is positive. 2) When 3 of the 4 integers share the same sign and all are non-zero (3 are positive and 1 is negative; or 3 are negative and 1 is positive)…
The set of positive integers contains 1 but not zero. Within the set of integers, there is the subset of positive integers, the subset of negative integers and the subset with a single element in it - zero. There are a zillion other sets that could be specified that meet the conditions set down in the question. The one cited is an easy one.
When the quotient of two integers is positive, either both integers are positive or both negative. When the quotient of two integers is negative, one of the integers is positive and one negative. When the quotient of two integers is zero, the first integer is zero and the second one is anything but zero.
Integers are the "counting numbers" and their negative counterparts, and zero. Opposite integers are the pairs of integers that have the same absolute value, or, in other words, are the same distance from zero. 10 and -10 are opposite integers. 43 and -43 are opposite integers. It's just that simple.