Which are partitions are for $\mathbb{Z}$? Which are covers for $\mathbb{Z}$? Which are both or neither?

127 Views Asked by Bumbble Comm At 27 Mar 2026 - 11:23

(a) {{x : x is an even integer}, {x : x is an odd integer}}

(b) {{x : x is an even integer}, {x : x is divisible by 3}}

Note - divisible by 3 includes negative integers, yes? -3, -6, -9, ... and so on?

(d) {{x : x is a negative integer }, {0}, {x : x is a positive integer}}

(e) {{x : x is an even integer}, {0}, {x : x is an odd integer}}

From my understanding...

(a) Partition (must be a cover).

(b) Not a cover / partition.

(d) A partition (must be a cover).

(e) Only a cover.