\[11\] is an indivisible number We realize that, the square base of any indivisible number is an unreasonable number. In this way \[\surd 11\] is a silly number Henceforth, the given assertion...

### Which of the following statements are true and which are false? In each case give a valid reason for saying so. (i) r: Circle is a particular case of an ellipse. (ii) s: If x and y are integers such that x > y, then –x < –y.

(i) The condition of an elipse is, In the event that we put\[~a\text{ }=\text{ }b\text{ }=\text{ }1\], we get \[{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }1,~\], which is a condition of a circle Thus,...

### 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 bisects each chord of the circle.

(I) The given assertion \[p\]is bogus. By the meaning of harmony, it ought to meet the circle at two particular focuses (ii) The given assertion \[q\]is bogus. The middle won't cut up that harmony...

### By giving a counter example, show that the following statements are not true. (i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle. (ii) q: The equation x^2 – 1 = 0 does not have a root lying between 0 and 2.

(I) Let \[q:\]All the points of a triangle are equivalent \[r:\]The triangle is an insensitive calculated triangle The given assertion \[p\]must be refuted. To show this, required points of a...

### Show that the following statement is true by the method of contrapositive. p: If x is an integer and x^2 is even, then x is also even.

Let \[p:\]If \[x\]is a number and \[{{x}^{2}}\]is even, then, at that point, \[x\]is likewise even Let \[q:\text{ }x\]is a number and \[~{{x}^{2}}~\]is even \[r:\text{ }x\]is even By contrapositive...

### Show that the statement “For any real numbers a and b, a^2 = b^2 implies that a = b” is not true by giving a counter-example.

The given assertion can be written as 'assuming' is given beneath Assuming \[a\text{ }and\text{ }b\]are genuine numbers to such an extent that \[{{a}^{2}}~=\text{ }{{b}^{2}},\text{ }a\text{...

### Show that the statement p: “If x is a real number such that x^3 + 4x = 0, then x is 0” is true by method of contrapositive

Let \[p:\]'In case \[x\]is a genuine number to such an extent that \[{{x}^{3}}\text{ }+\text{ }4x\text{ }=\text{ }0,\]then, at that point, \[x\text{ }is\text{ }0'\] \[q:\text{ }x\]is a genuine...

### Show that the statement p: “If x is a real number such that x^3 + 4x = 0, then x is 0” is true by (i) direct method (ii) method of contradiction

Let \[p:\]'In case \[x\]is a genuine number to such an extent that \[{{x}^{3}}\text{ }+\text{ }4x\text{ }=\text{ }0,\]then, at that point, \[x\text{ }is\text{ }0'\] \[q:\text{ }x\]is a genuine...