Advertisements
Advertisements
प्रश्न
Read the following axioms:
- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.
Advertisements
उत्तर
Some of Euclid’s axioms are
- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- Things which are double of the same things are equal to one another.
Thus, given three axioms are Euclid’s axioms. So, here we cannot deduce any statement from these axioms which contradicts any axiom. So, given system of axioms is consistent.
APPEARS IN
संबंधित प्रश्न
Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?
line segment
If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
Given three distinct points in a plane, how many lines can be drawn by joining them?
In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio ______.
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
The things which are double of the same thing are equal to one another.
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom.
Read the following statements which are taken as axioms:
- If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
- If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
The following statement is true or false? Give reason for your answer.
If two circles are equal, then their radii are equal.
