Five different ways to write the above given statement are: (I) A triangle is equiangular shows that it is an obtuse angled triangle . (ii) A triangle is equiangular provided that the triangle is a...
Check the validity of the statements given below by the method given against it. (i) p: The sum of an irrational number and a rational number is irrational (by contradiction method). (ii) q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).
(I) The given assertion is as per the following p: The amount of a silly number and a judicious number is silly. Allow us to expect that the assertion \[p\] is bogus. That is, The amount of a...
Given below are two statements p: 25 is a multiple of 5. q: 25 is a multiple of 8. Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
The compound assertion with \['And'\] is as per the following \[25\]is a various of \[5\text{ }and\text{ }8\] This is bogus articulation since \[25\] is definitely not a numerous of \[8\] The...
Re write the following statements in the form “p if and only if q”. r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
A quadrilateral is equiangular if by some stroke of good luck in case it is a square shape.
Re write each of the following statements in the form “p if and only if q”. (i) p: If you watch television, then your mind is free and if your mind is free, then you watch television. (ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
(I) You stare at the TV if and provided that your brain is free (ii) You get A grade if and provided that you do all the schoolwork consistently
Write the statement in the form “if p, then q”. r: You can access the website only if you pay a subscription fee.
The assertion\[~r\] in the structure 'assuming' is as per the following Assuming you can get to the site, you pay a membership charge.
Write each of the statements in the form “if p, then q”. (i) p: It is necessary to have a password to log on to the server. (ii) q: There is traffic jam whenever it rains.
(I) The assertion p in the structure 'on the off chance that' is as per the following Assuming you sign on to the worker, you have a secret word. (ii) The assertion \[q\]in the structure 'assuming'...
State the converse and contrapositive of the following statement : r: If it is hot outside, then you feel thirsty.
The opposite of proclamation r is given underneath On the off chance that you feel parched, it is hot outside. The contrapositive of proclamation r is given underneath On the off chance that you...
State the converse and contrapositive of each of the following statements: (i) p: A positive integer is prime only if it has no divisors other than 1 and itself. (ii) q: I go to a beach whenever it is a sunny day.
(I) Statement \[p\]can be written in the structure 'assuming' is as per the following Assuming a positive number is prime, it has no divisors other than \[1\] and itself The opposite of the...
Write the negation of the following statements: (i) r: For every real number x, either x > 1 or x < 1. (ii) s: There exists a number x such that 0 < x < 1.
Solution:- (I) The nullification of articulation \[r\] is given underneath There exists a genuine number \[~x\], to such an extent that neither \[x\text{ }>\text{ }1\text{ }nor\text{ }x\text{...
Write the negation of the following statements: (i) p: For every positive real number x, the number x – 1 is also positive. (ii) q: All cats scratch.
(I) The nullification of explanation \[p\]is given beneath There exists a positive genuine number\[x\], to such an extent that \[x\text{ }\text{ }1\]isn't positive (ii) The invalidation of...