Write the negation of the following statements:
(i) p: For every real number `x, x^(2)gtx`.
(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 elementary level.

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

Write the negation of the following statements: s: There exists a number x such that 0 < x < 1.

Write the equation of the following mathematical statements A number x decreased by 5 is 14

Identify the quantifier in the following statements and write the negation of the statements. For every real number x, x is less than x + 1.

Are the following pairs of statements negations of each other: The number x is not a rational number. The number x is not an irrational number.

Write all the factors of the following numbers. i. 36 ii. 23 iii. 96 iv. 115

Restate the following statements with appropriate conditioins, so that they become true statements. i. For every real number x, 3x gt x . ii. For every real number x, x^(2) ge x iii. If you divide a number by two, you will always get half of that number. iv. The angle subtended by a chord of a circle at a point on the circle is 90°. v. If a quadrilateral has all its sides equal, then it is a square.

Let h(x)=f(x)-(f(x))^(2)+(f(x))^(3) for every real number x . Then

Restate the following statements with appropriate conditioins, so that they become true statements. For every real number x , x^(2) ge x .