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
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
In how many points two distinct lines can intersect?
In how many points two distinct planes can intersect?
Euclid divided his famous treatise “The Elements” into ______.
The side faces of a pyramid are ______.
In ancient India, the shapes of altars used for household rituals were ______.
‘Lines are parallel, if they do not intersect’ is stated in the form of ______.
The statements that are proved are called axioms.
Solve the following question using appropriate Euclid’s axiom:
Look at the figure. Show that length AH > sum of lengths of AB + BC + CD.
The following statement is true or false? Give reason for your answer.
There are an infinite number of lines which pass through two distinct points.
