Home
Class 11
MATHS
Statement : if a natural number is even,...

Statement : if a natural number is even, then is square is also even.
write this statement in 5 different forms of the same meaning.

Text Solution

Verified by Experts

(1).(i) a natural number is even imlies that its square is even.
(ii) a natural number is even only if its square is even.
(iii) for a natural number to be even it is necessary that its square is even.
(iv) for the square of a natural number to be even it is sufficient the number is even.
(v) if the square of a natural number is not even, then the natural number is not even.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14E|6 Videos

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14.1|2 Videos

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 14C|4 Videos

  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|14 Videos

  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|11 Videos

Similar Questions

Explore conceptually related problems

The statement '' If x^(2) is not even, then x is not even '' is coverse of the statement

p : if a natural is odd , then its sqare also odd. Which of the following does not convey the same meaning as that by statement p

A= { x: x is a natural number} B= {x: x is an even natural number} find A intersection B

Given below are two statements p : Cube of an even number is even q : Cube of an odd number is odd Write the compound statement connecting these two statement with "and" and checks its validity

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.

Write the converse of the following statements: (i)If a number is even then n^2 is even (ii)If you do all the exercises in the book, you get an A grade in the class.

p : If end digit of an integer is 5 then end digit of its square is also 5. Statement p is same as the

By taking three different values of n verify the truth of the following statements: If n is even, then n^3 is also even. if n is odd, then n^3 is also odd. If n leaven remainder 1 when divided by 3, then n^3 also leaves 1 as remainder when divided by 3. If a natural number n is of the form 3p+2\ t h e n\ n^3 also a number of the same type.

Write the contrapositive of the following statements: (i)If x is prime number then x is odd (ii)If two lines re parallel then they do not intersect in the same plane. (iii) x is even number implies that x is divisible by 4.

If the variance of first n even natural numbers is 133, then the value of n is equal to