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Fundamental Theorem of Arithmetic

Write the con...

Question

Write the converse of: If a number has more than two divisors then it is a composite number. [1 Mark]

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Solution

The converse of given conditional statement is : If the number is composite, then it has more than two factors. [1 Mark]

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Q. 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
(iii) r : If it is hot outside then you feel thirsty

State the converse and contrapositive of each of the following statements :

(i) If it is hot outside, then you feel thirsty.

(ii) I go to a beach whenever it is a sunny day.

(iii) A spositive integer is prime only if it has no divisors other than 1 and itself.

(iv) If you live in Delhi, then you have winter clothes.

(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Q. State the converse and contrapositive of each of the following statements:
(i) If it is hot outside, then you feel thirsty.
(ii) I go to a beach whenever it is a sunny day.
(iii) A positive integer is prime only if it has no divisors other than 1 and itself.
(iv) If you live in Delhi, then you have winter clothes.
(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Q. A composite number always has more than two distinct factors.

Q. The smallest positive divisor greater than 1 of a composite number 'a' is ______

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