Mathematics
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.
Related Questions
State whether the following statements are always true, always false or ambiguous. Justify your answers.
(i) All mathematics textbooks are interesting.
(ii) The distance from the Earth to the Sun is approximately 1.5 × 108 km.
(iii) All human beings grow old.
(iv) The journey from Uttarkashi to Harsil is tiring.
(v) The woman saw an elephant through a pair of binoculars.
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.
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.
Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?