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) x2 + 5|x| + 6 = 0 has no real roots.
(ix) This sentences is a statement.
(x) Is the earth round?
(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) x2 + 5|x| + 6 = 0 has no real roots.
Firstly, let us solve the given expression.
If x>0,
x2+5|x|+6=0
x2+5x+6=0
x = -3 or x = -2
Since x>0, the equation has no roots.
If x<0,
x2+5|x|+6=0
x2 – 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 x2 is irrational, then x is rational.” The statement is true because the number x2 = π2 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 n2 is even”
Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x2 is odd, then x is also odd.”