Question

If A is the set of all positive integers and B is the set of all negative integers, then $A \cup B$ is
A) The set of all integers
B) \left\\{ 0 \right\\}
C) The set of all integers except zero
D) None of these

Answer 1

Set A = {Z^ + } = \left\\{ {1,2,3,4........} \right\\} and set B = {Z^ - } = \left\\{ { - 1, - 2, - 3, - 4........} \right\\} and $A \cup B$is the combination of set A and set B then A \cup B = \left\\{ {....... - 3, - 2, - 1,1,2,3,.......} \right\\}then $A \cup B$ contains all integers except zero.

Complete step by step solution:
Given A is the set of all positive integers
Therefore A = {Z^ + } = \left\\{ {1,2,3,4........} \right\\}
And B is the set of all negative integers
Therefore B = {Z^ - } = \left\\{ { - 1, - 2, - 3, - 4........} \right\\}
Now, $A \cup B$ is the combination of set A and B
Therefore A \cup B = \left\\{ {....... - 3, - 2, - 1,1,2,3,.......} \right\\}
Hence, $A \cup B$ is set of all integers except zero.

Hence, Option C is the correct option.

Note:
Set of all positive integers {Z^ + } = \left\\{ {1,2,3,4........} \right\\}and set of all negative integers are {Z^ - } = \left\\{ { - 1, - 2, - 3, - 4........} \right\\}. Zero does not belong to any set hence zero is neither positive nor negative integers.