Question

Which of the following sets is a universal set for the other four sets?
(a) The set of even natural numbers
(b) The set of odd natural numbers
(c) The set of natural numbers
(d) The set of negative numbers
(e) The set of integers

• A. $\left(e\right)$
• B. $\left(a\right)$
• C. $\left(b\right)$
• D. $\left(c\right)$

Answer 1

The correct option is A $\left(e\right)$

We know that $N\subset Z$ where $N$ represents set of natural numbers and $Z$ represents set of all positive and negative integers.
Since $N\subset Z$,
$\left(a\right),\left(b\right),\left(c\right)$ are subsets of $\left(e\right)$ $...\left(1\right)$
Since $Z$ represents set of all positive and negative integers.
$\left(d\right)$ is a subset of $\left(e\right)$ $...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$ we get
$\left(a\right),\left(b\right),\left(c\right),\left(d\right)$ are subsets of $\left(e\right)$.
Hence $\left(e\right)$ is the universal set for the other four sets.