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.
(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 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.”