The set X = A × Z × A × (Q ∖ Z) is a Cartesian product of four sets: the set of lower-case English alphabet letters A, the set of integers Z, again the set of lower-case English alphabet letters A, and the set of rational numbers Q excluding integers Z.

A subset of X that has exactly five elements can be represented in set-roster notation as follows:

Let's denote the subset as S.

S = {('a', 1, 'b', 1/2), ('c', 2, 'd', 2/3), ('e', 3, 'f', 3/4), ('g', 4, 'h', 4/5), ('i', 5, 'j', 5/6)}

Here, each element of the subset S is an ordered 4-tuple, where the first and third components are from the set A (lower-case English alphabet), the second component is from the set Z (integers), and the fourth component is from the set Q ∖ Z (rational numbers excluding integers).

This subset S has exactly five elements, as required.

Question

The set X = A × Z × A × (Q ∖ Z) is a Cartesian product of four sets: the set of lower-case English alphabet letters A, the set of integers Z, again the set of lower-case English alphabet letters A, and the set of rational numbers Q excluding integers Z.

A subset of X that has exactly five elements can be represented in set-roster notation as follows:

Let's denote the subset as S.

S = {('a', 1, 'b', 1/2), ('c', 2, 'd', 2/3), ('e', 3, 'f', 3/4), ('g', 4, 'h', 4/5), ('i', 5, 'j', 5/6)}

Here, each element of the subset S is an ordered 4-tuple, where the first and third components are from the set A (lower-case English alphabet), the second component is from the set Z (integers), and the fourth component is from the set Q ∖ Z (rational numbers excluding integers).

This subset S has exactly five elements, as required.

Knowee AI · Accepted Answer

The set X = A × Z × A × (Q ∖ Z) is a Cartesian product of four sets: the set of lower-case English alphabet letters A, the set of integers Z, again the set of lower-case English alphabet letters A, and the set of rational numbers Q excluding integers Z.

A subset of X that has exactly five elements can be represented in set-roster notation as follows:

Let's denote the subset as S.

S = {('a', 1, 'b', 1/2), ('c', 2, 'd', 2/3), ('e', 3, 'f', 3/4), ('g', 4, 'h', 4/5), ('i', 5, 'j', 5/6)}

Here, each element of the subset S is an ordered 4-tuple, where the first and third components are from the set A (lower-case English alphabet), the second component is from the set Z (integers), and the fourth component is from the set Q ∖ Z (rational numbers excluding integers).

This subset S has exactly five elements, as required.

Let A denote the lower-case English alphabet {a, b, c, . . . , z} and let X = A × Z × A × (Q ∖ Z). Use set-roster notation to give an example of a subset of X that has exactly five elements.

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