Home
Class 11
MATHS
State the converse and contrapositive of...

State the converse and contrapositive of each of the following statements:
p: A positive integer is prime only if it has no divisors other than 1 and itself.

Text Solution

Verified by Experts

The correct Answer is:
The statement can be written as ''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.
Promotional Banner

Similar Questions

Explore conceptually related problems

State the converse and contrapositive of each of the following statements: r: If it is hot outside, then you feel thirsty.

State the converse and contrapositive of each of the following statements: q: I go to a beach whenever it is a sunny day.

Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd.

State the property that is used in each of the following statements: If a||b, lfoor1=lfloor5

Write the contrapositive and converse of the following statements. Something is cold implies that it has low temperature.

Write the negation of the following statements: p: For every positive real number x, the number x - 1 is also positive.

Find counter - examples to disprove the following statements : n^(2)-n+41 is a prime for all positive integers n.

By giving counter example, show that the following statement is false. P : If n is an odd integer, then n is prime

Write the component statement of the following compound statement and check whether the given compound statement is true or false "0 is less than every positive integer and every negative integer.

State the abscissa and originate of the following points and describe the position of each point (i) P(8,8) (ii) Q(6,-8).