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

Hint:
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.