(i) The component statements are
(a) Number 3 is prime
(b) Number 3 is odd
Here, both the statements are true
(ii) The component statements are
(a) All integers are positive
(b) All integers are negative
Here, both the statements are false.
(iii) The component statements are
(a) 100 is divisible by 3
(b) 100 is divisible by 11
(c) 100 is divisible by 5
Here, the statements (a) and (b) are false and (c) is true.
Answered by Abhisek | 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.”