Find the component statements of the following compound statements:
(i) The sky is blue, and the grass is green.
(ii) The earth is round, or the sun is cold.
(iii) All rational numbers are real, and all real numbers are complex.
(iv) 25 is a multiple of 5 and 8.
(i) The components of the compound statement are:
P: The sky is blue.
Q: The grass is green.
(ii) The components of the compound statement are:
P: The earth is round.
Q: The sun is cold.
(iii) The components of the compound statement are:
P: All rational number is real.
Q: All real number are complex.
(iv) The components of the compound statement are:
P: 25 is multiple of 5.
Q: 25 is multiple of 8.
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.”