Related InterviewSolutions

• Statement : if a natural number is even, then is square is also even. write this statement in 5 different forms of the same meaning.
• Identify the quantifier in the following statements and write thenegation of the statements.(i) There exists anumber which is equal to its square.(ii) For every realnumber x, x is less than `x" "+" "1`.(iii) There exists acapital for e
• Identify the quantifers used in the following statements and write the negation of the statements : (i) there exists a number which is equal to its cube. (ii) for all states in india, there is a capital in india. (iii) there exists a man whose age is 150 years. (iv) all students are of 25 years or more.
• Write the negation of the following statements:(i) p: For every real number `x ,``x^2> x`.(ii) q: There exists a rational number x such that `x^2=2`.(iii) r: All birds have wings.(iv) s: All students study mathematics at the element
• Write the negation of the following statements:(i) p : For every positive real number x, the number `x - 1`is also positive.(ii) q : All cats scratch.(iii) r : For every real number x, either `x > 1`or `x < 1`.(iv) s : There exist
• Prove that `sqrt(2)`is an irrational number.
• Given below are two statementsp : 25 is a multiple of5.q : 25 is a multiple of8.Write the compound statements connecting these two statements with"And" and "Or". In both cases check the validity of thecompound statement.
• Show that the statement p: If x is a real number such that `x^3+4x=0`. then x is 0 is true by(i) direct method, (ii) method of contradiction,(iii) method of contrapositive.
• Verify by the method of contradiction. `p:sqrt(7)`is irrational.
• Check the validity of the statements given below by the method given against it.(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).(ii) q: If n is a real number with `n > 3`, then `n^2>9