Sivaang made the statement "a prime number is always odd”. Dylan replied "2 is a prime number and its an even number”. By which method did Dylan validate/disprove Sivaang's statement?

Direct

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Contrapositive

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Contradiction

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None of these

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Solution

The correct option is C
Contradiction

Dylan's statement counters Sivaang's statement. If Dylan's statement is true, then he has disproved Sivaang's statement by giving a counterexample.

We need to check if Dylan's statement is true. He says, "2 is a prime number and its an even number". This statement is indeed true.

Hence Dylan disproves Sivaang's statement by the giving a counterexample.

Suggest Corrections

Similar questions

State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

Question 16
The product of a non-zero whole number and its successor is always

(A) an even number
(B) an odd number
(C) a prime number
(D) divisible by 3

Q. Which of the following statements are true?
(i) 1 is the smallest prime number.
(ii) If a number is prime, it must be odd.
(iii) The sum of two prime numbers is always a prime number.
(iv) If two numbers are co-primes, at least one of them must be a prime number.

Q. To prove "" All prime numbers are not odd." we showed that "

2

is even and prime"
This method is

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

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