Answer the following questions:-

**(i) **All birds sing.

**(ii)** Some even integers are prime.

**(iii) **There is a complex number which is not a real number.

**(iv)** I will not go to school.

**(v)** Both the diagonals of a rectangle have the same length.

**(vi) **All policemen are thieves.

Asked by Aaryan | 1 year ago | 48

**(i) **All birds sing.

The negation of the statement is:

It is false that “All birds sing.”

Or

“All birds do not sing.”

**(ii) **Some even integers are prime.

The negation of the statement is:

It is false that “even integers are prime.”

Or

“Not every even integers is prime.”

**(iii) **There is a complex number which is not a real number.

The negation of the statement is:

It is false that “complex numbers are not a real number.”

Or

“All complex number are real numbers.”

**(iv) **I will not go to school.

The negation of the statement is:

“I will go to school.”

**(v) **Both the diagonals of a rectangle have the same length.

The negation of the statement is:

“There is at least one rectangle whose both diagonals do not have the same length.”

**(vi) **All policemen are thieves.

The negation of the statement is:

“No policemen are thief”.

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.”