Write each of the following statement in the form “if-then”.

**(i)** You get a job implies that your credentials are good.

**(ii)** The Banana trees will bloom if it stays warm for a month.

**(iii)** A quadrilateral is a parallelogram if its diagonals bisect each other.

**(iv)** To get A^{+} in the class, it is necessary that you do the exercises of the book.

Asked by Pragya Singh | 1 year ago | 100

**(i)** If you get a job, then your credentials are good.

**(ii) **If the Banana trees stays warm for a month, then the trees will bloom.

**(iii)** If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

**(iv)** If you want to score an A^{+} in the class, then you do all the exercises of the book.

Determine 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.”