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, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
How many least number of distinct points determine a unique plane?
How many planes can be made to pass through three distinct points?
Boundaries of solids are ______.
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is ______.
Greek’s emphasised on ______.
Solve the following question using appropriate Euclid’s axiom:
Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have AC = DC, CB = CE. Show that AB = DE.
Solve the following question using appropriate Euclid’s axiom:
In the following figure, if OX = `1/2` XY, PX = `1/2` XZ and OX = PX, show that XY = XZ.
