Restate the following statements with appropriate conditions, so that they become true. (i) If a^2 b^2 , then a b. (ii) If x^>2 = y^2 , then x = y. (iii) If (x + y)^2 = x^2 + y^2 , then x = 0. (iv) The diagonals of a quadrilateral bisect each other.

(i) If a 0 and a 2 b 2 , then a b. (ii) If xy 0 and x 2 = y 2 , then x = y. (iii) If (x + y) 2 = x 2 + y 2 and y 0 , then x = 0. (iv) The diagonals of a parallelogram bisect each other.

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Mathematics

Restate the following statements with appropriate conditions, so that they become true.
(i) If a² > b², then a > b.
(ii) If x² = y², then x = y.
(iii) If (x + y)² = x² + y², then x = 0.
(iv) The diagonals of a quadrilateral bisect each other.

Mathematics Proofs

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Answer

(i) If a > 0 and a² > b², then a > b.

(ii) If xy ≥ 0 and x² = y², then x = y.

(iii) If (x + y)² = x² + y² and y ≠ 0, then x = 0.

(iv) The diagonals of a parallelogram bisect each other.

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Mathematics

Restate the following statements with appropriate conditions, so that they become true.
(i) If a² > b², then a > b.
(ii) If x² = y², then x = y.
(iii) If (x + y)² = x² + y², then x = 0.
(iv) The diagonals of a quadrilateral bisect each other.

Mathematics Proofs

Answer

Related Questions

State whether the following statements are true or false. Justify your answers.
(i) All hexagons are polygons.
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(iv) Some real numbers are irrational.
(v) Not all real numbers are rational.

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(i) Both a and b must be zero.
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(iii) Either a or b must be non-zero.

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

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Mathematics

Restate the following statements with appropriate conditions, so that they become true.(i) If a2 > b2, then a > b.(ii) If x2 = y2, then x = y.(iii) If (x + y)2 = x2 + y2, then x = 0.(iv) The diagonals of a quadrilateral bisect each other.

Mathematics Proofs

Answer

Related Questions

State whether the following statements are true or false. Justify your answers.(i) All hexagons are polygons.(ii) Some polygons are pentagons.(iii) Not all even numbers are divisible by 2.(iv) Some real numbers are irrational.(v) Not all real numbers are rational.

Let a and b be real numbers such that ab ≠ 0. Then which of the following statements are true? Justify your answers.(i) Both a and b must be zero.(ii) Both a and b must be non-zero.(iii) Either a or b must be non-zero.

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

Given that the product of two rational numbers is rational, and suppose a and b are rationals, what can you conclude about ab?

Restate the following statements with appropriate conditions, so that they become true.
(i) If a² > b², then a > b.
(ii) If x² = y², then x = y.
(iii) If (x + y)² = x² + y², then x = 0.
(iv) The diagonals of a quadrilateral bisect each other.

State whether the following statements are true or false. Justify your answers.
(i) All hexagons are polygons.
(ii) Some polygons are pentagons.
(iii) Not all even numbers are divisible by 2.
(iv) Some real numbers are irrational.
(v) Not all real numbers are rational.

Let a and b be real numbers such that ab ≠ 0. Then which of the following statements are true? Justify your answers.
(i) Both a and b must be zero.
(ii) Both a and b must be non-zero.
(iii) Either a or b must be non-zero.