Find out which of the following sentences are statements and which are not. Justify your answer.

**(i) **Listen to me, Ravi!

**(ii) **Every set is a finite set.

**(iii)** Two non-empty sets have always a non-empty intersection.

**(iv)** The cat pussy is black.

**(v) **Are all circles round?

**(vi)** All triangles have three sides.

**(vii) **Every rhombus is a square.

**(viii)** x^{2} + 5|x| + 6 = 0 has no real roots.

**(ix) **This sentences is a statement.

**(x)** Is the earth round?

Asked by Aaryan | 1 year ago | 51

**(i) **Listen to me, Ravi!

The sentence “Listen to me, Ravi! “Is an exclamatory sentence.

∴ It is not a statement.

**(ii) **Every set is a finite set.

This sentence is always false, because there are sets which are not finite.

∴ It is a statement.

**(iii) **Two non-empty sets have always a non-empty intersection.

This sentence is always false, because there are non-empty sets whose intersection is empty.

∴ It is a statement.

**(iv) **The cat pussy is black.

There are some cats which are black, and not black, So, the given sentence may or may not be true.

∴ It is not a statement.

**(v) **Are all circles round?

The given sentence is an interrogative sentence.

∴ It is not a statement.

**(vi) **All triangles have three sides.

The given sentence is a true declarative sentence.

∴ It is a true statement.

**(vii) **Every rhombus is a square.

This sentence is always false, because Rhombuses are not a square.

∴ It is a statement.

**(viii) **x^{2} + 5|x| + 6 = 0 has no real roots.

Firstly, let us solve the given expression.

If x>0,

x^{2}+5|x|+6=0

x^{2}+5x+6=0

x = -3 or x = -2

Since x>0, the equation has no roots.

If x<0,

x^{2}+5|x|+6=0

x^{2} – 5x+6=0

Since x<0, the equation has no real roots.

∴ It is a statement.

**(ix) **This sentences is a statement.

The statement is not indicating the correct value, hence we can say that value contradicts the sense of the sentence.

∴ It is not a statement.

**(x) **Is the earth round?

The given sentence is an interrogative sentence.

∴ It is not a statement.

Answered by Sakshi | 1 year agoDetermine whether the argument used to check the validity of the following statement is correct: p: “If x^{2} is irrational, then x is rational.” The statement is true because the number x^{2} = π^{2} is irrational, therefore x = π is irrational.

Which of the following statements are true and which are false? In each case give a valid reason for saying so

**(i)** p: Each radius of a circle is a chord of the circle.

**(ii) **q: The centre of a circle bisect each chord of the circle.

**(iii)** r: Circle is a particular case of an ellipse.

**(iv)** s: If x and y are integers such that x > y, then – x < – y.

**(v)** t: \( \sqrt{11}\) is a rational number.

By giving a counter example, show that the following statement is not true. p: “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”

Show that the following statement is true “The integer n is even if and only if n^{2} is even”

Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x^{2} is odd, then x is also odd.”