Question

State whether the following statement is true or false-
Every integer is a natural number.

Answer 1

Hint: We will try to understand each and every word in the statement and then proceed with the answer. Natural numbers are a set of non-decimal numbers which are greater than zero. Integers are a set of non-decimal numbers which can be positive, zero or negative.

Complete step-by-step answer:
The given statement is that-
Every integer is a natural number.

We know that integers are a set of non-decimal numbers which can be positive, zero or negative. They can be represented as-
${\text{I}} = \left\{ { - \infty ,\;...,\; - 3,\; - 2,\; - 1,\;0,\;1,\;2,\;3,\;...,\;\infty } \right\}$

We also know that natural numbers are a set of non-decimal numbers which are greater than zero. They can be represented as-
${\text{N}} = \left\{ {1,\;2,\;3,\;....,\;\infty } \right\}$

We can clearly see that all the elements in the set N, are present in the set I. This means that the set N is a subset of I. In other words, every natural number is also an integer.

But we can see that all the elements in set I are not present in set N, this means that all integers are not natural numbers. For example, -3 is an integer but not a natural number.

Hence, the given statement, ‘Every integer is a natural number’ is FALSE.

Note: In such types of questions, we need to pay close attention to each and every word in the statement. Also, we can check the statements using suitable examples that contradict or support the statement.