Question

State whether the following statements are true(T) or False(F):
\[0\] is greater than every negative integer.
a). True
b). False

Answer 1

Hint: The given statement can be solved by evaluating the statement. The statement is true if \[0\] is greater than every negative integer. The statement is not true i.e., false if \[0\] is not greater than every negative integer. To prove the statement is true we need to prove that there is no integer such that it is greater than \[0\]. We prove this by contradiction.

Complete step-by-step solution:
Let us consider there is a negative integer $-x$ such that $-x>0$
However, the definition of the negative integer is that the integer which is less value than \[0\] .
Hence a whole number say $y$ which is called negative integer is always less than \[0\].
But as we considered the inequality as $-x>0$.
This statement is wrong unless $x$ is a negative number such that $-x$ is a positive number.
Hence the given statement \[0\] is greater than every negative integer is correct.
Therefore, the statement is true which is given by option (1).

Additional information: The integers are numbers which do not have any fractional components. The whole numbers consist of positive integers and zero. These do not consist of fractional numbers and negative integers. Natural numbers are a part of whole numbers as natural numbers do not include zero but it consists of positive integers.

Note: The given statement in question is said to be true if the given statement represents the real case. The statement is said to be false if the given statement represents the unreal case. In the above case the given statement represents the real case and hence it is the true statement.