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H Harsh Kankaria
 a.) A triangle is equiangular implies it is an obtuse angled triangle. b.) Knowing that a triangle is equiangular is sufficient to conclude that it is an obtuse angled triangle. c.) A triangle is equiangular only if it is an obtuse angled triangle. d.) When a triangle is equiangular, it is necessarily an obtuse angled triangle. e.) If a triangle is not an obtuse-angled triangle, it is not equiangular.

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H Harsh Kankaria
Assume that the given statement q is false. The statement becomes: If n is a real number with n > 3, then . Therefore n>3 and n is a real number. This is a contradiction. Therefore our assumption is wrong. Thus, the given statement q is true.

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H Harsh Kankaria
Assume that the given statement p is false. The statement becomes: The sum of an irrational number and a rational number is rational. Let   Where  is irrational number and  and are rational numbers.    is a rational number and is an irrational number, which is not possible. This is a contradiction. Hence our assumption is wrong. Thus, the given statement p is true.

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H Harsh Kankaria
Given, p:  25 is a multiple of 5. q:  25 is a multiple of 8. p is true while q is false. The compound statement with 'And' is:  25 is a multiple of 5 and 8.  This is a false statement. The compound statement with 'Or' is:  25 is a multiple of 5 or 8. This is a true statement.

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H Harsh Kankaria
The statement in the form “p if and only if q” is : You get an A grade if and only if you do all the homework regularly.

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H Harsh Kankaria
The statement in the form “if p, then q” is : If you can access the website, then you pay a subscription fee.

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H Harsh Kankaria
The statement in the form “if p, then q” is : If it rains, then there is a traffic jam.

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H Harsh Kankaria
The statement in the form “if p, then q” is : If you log on to the server, then you have a password.

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H Harsh Kankaria
The given statement is in the form "if p then q". The converse of the statement is: If you feel thirsty, then it is hot outside. The contrapositive of the statement is: If you don't feel thirsty, then it is not hot outside.

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H Harsh Kankaria
The given statement as "if-then" statement is: If it is a sunny day, then I go to a beach. The converse of the statement is: If I go to the beach, then it is a sunny day. The contrapositive of the statement is: If I don't go to the beach, then it is not a sunny day.

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H Harsh Kankaria
The given statement as "if-then" statement is:  If a positive integer is prime, then it has no divisors other than 1 and itself. The converse of the statement is: If a positive integer has no divisors other than 1 and itself, then it is a prime. The contrapositive of the statement is: If positive integer has divisors other than 1 and itself then it is not prime.

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H Harsh Kankaria
The negation of the statement is: There does not exist a number x such that 0 < x < 1.

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H Harsh Kankaria
The negation of the statement is: It is false that all cats scratch. Or There exists a cat which does not scratch.  

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H Harsh Kankaria
The negation of the statement is: There exists a positive real number x such that x–1 is not positive.  
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