Exercise 14.5

### Which of the following statements are true and which are false? In each case give a valid reason for saying so. t: √11 is a rational number.

$11$ 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...

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{... read more ### 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...
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...