Question

Which of the following is not a statement?
(a) Every set is a finite set.
(b) Every square is a rectangle.
(c) The sun is a star.
(d) Shut the window.

Answer 1

Hint: There are 4 normal mathematical statements. Look at them one-by-one, then find which of them is not a statement. Prove that one has neither true value nor false value to make it a non-statement. Take the statements one by one and prove them with examples. If you are neither able to prove nor disprove then that expression is not a statement.

Complete step-by-step answer:
A statement is defined as the one that has got the truth value.
A statement will either have truthfulness or falsity.
It will be either true or false.

Statement-A: False
Set: In mathematics, a set is a well-defined collection of distinct objects. The arrangement of objects does not matter.
Finite set: Set with a finite set of objects is called a finite set.
So the set of natural numbers is an example for the contradiction of statement-1.

Statement-B: True
A square is quadrilateral with all four angles to be 90 and all side lengths are equal.
A rectangle is quadrilateral with all four angles to be 90 and opposite sides are of equal lengths.
So the square satisfies the conditions of the rectangle. So the square is a special kind of rectangle.
Thus all squares are rectangles.

Statement-C: True
The sun is defined as a star which is the center of our solar system. So obviously the statement is true.
In given options A, B and C denote comments, which are correctly true or false.
D is a line which is a command that cannot be categorized as a statement because it is neither true nor false.
So, D is not a statement.
Option (d) is the answer.

Note: Be careful while taking all statements and taking definitions of set and finite set.
Find the difference between them. The statement C is not mathematical but it has a truth value so it can be categorized under the category statement.