Question

Consider the sentence : $
  x < 5 \\
    \\
  $
Which of the following integers make this open sentence true?
A. 4
B. 5
C. 6
D. None of the above

Answer 1

Hint: Open sentence means a statement which contains one or more variables and conditions so given are true or false.
 In this question we have a variable which is mentioned under a condition , we will check out options for the integer that is less than 5.

Complete step-by-step answer:
Our sentence is $
  x < 5 \\
    \\
  $ it is also said as x is less than 5 .
Therefore we have 1,2,3,4 as integers which satisfy the condition given.
First option is 4
It is less than 5 and it fulfils the statement given to us
Second option is 5
We can see that as per condition we have $
  x < 5 \\
    \\
  $
This option is not correct because there should be an equal sign for this option .
Third option is 6
We know that 6 is greater than 5 and if we want to write it then it can be written as
Mathematically $6 > 5$
Therefore this is also an incorrect option.
Last option is none of the above

After discussing all the options we conclude that the correct option is A.

Note: One may get confused after reading the question how many integers are there and will answer in that manner so take little extra care over here.
Open sentences are easy to solve and results can be concluded but one should have knowledge of different types of symbols of equality (=) and inequalities .

The equations in which we have inequality symbols such as $ < , > , \leqslant , \geqslant $ then meanings are as follows:
$ < $ less than
$ > $ greater than
$ \leqslant $ less than equal to
$ \geqslant $ greater than equal to
Linear inequalities are used especially in graphical conditions.