Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b: a is sister of b} is the empty relation and R' = {(a, b: the difference between heights of a and b is less than 3 meters} is the universal relation.

-

Example 1: Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b: a is sister of b} is the empty relation and R' = {(a, b: the difference between heights of a and b is less than 3 meters} is the universal relation. 


Ans: Since, the school is boys school, no student of the school can be sister of any student of the school. Hence, R = ∅,  showing that R is the empty relation. It is also obvious that the difference between heights of any two students of the school has to less than 3 metres. This shows that R' = A X A is the universal relation.

Comments

  1. Mahi gupta10 June 2021 at 12:08

    Hey there! I could have sworn I’ve been to this website before but after checking through some of the post I realized it’s new to me. Anyways, I’m definitely happy I found it and I’ll be book-marking and checking back frequently!

    ReplyDelete

Post a Comment

Popular posts from this blog

QUANTUM NUMBERS (Principal, Azimuthal, Magnetic and Spin)

-
Image
                  QUANTUM NUMBERS  Orbitals represent regions in the space around the nucleus where the probability of finding the electron is maximum. A large number of electron orbitals are possible in atom. These can be distinguished by their size, shape and orientation of the orbitals. To describe each electron in an atom in different orbitals, we need a set of three numbers known as quantum numbers. These are designated as n, l and m. In addition to these three numbers another quantum number is also needed which specifies the spin of the electron. These four numbers are called quantum numbers. These are discussed below: 1. Principal quantum number (n) :  This quantum number determines the main energy shell or level in which the electron is present. It is denoted by n. It can have whole number values starting from 1 such as n = 1, 2, 3, 4 ... This quantum number also identifies as shell. The shell with n 1 is called the first sh...
Read more

Diagonal Relationship between Beryllium and Aluminium || Relation between Beryllium and Aluminium

-
  Diagonal Relationship between Beryllium and Aluminium The ionic radius of Beryllium (Be 2+) is estimated to be nearly 31 pm; the charge/radius ratio Or e/m ratio is nearly the same as that of the Al 3+ ion. Hence beryllium resembles aluminium in these ways. Some of the similarities are given below: » Like Aluminium, Beryllium(be) is not readily attacked by acids H+ donor because of the formation of an oxide film on the surface of the metal by reacting with oxygen, i.e. they are rendered passive by nitric acid. » Beryllium hydroxide[[Be(OH)4]2] dissolves in excess of alkali to give a beryllate ion, [ Be(OH)4]2– just as aluminium hydroxide[Al(OH)3] gives aluminate ion, [Al(OH)4] » The chlorides of metals beryllium and aluminium have Cl– bridged chloride structure in vapour phase. Both the chlorides are soluble in organic solvents and are strong as Lewis acids They are used as Friedel Craft catalysts. » Beryllium(Be) and aluminium(Al) ions have strong tendency to form complexes, (Be...
Read more

Math question

-
Image
A tower, x metre, has a flagstaff at its top. The tower and flagstaff subtends equal angles at a point distant y metre from the foot of the tower. Then find the length of the flagstaff ( in metre). 
Read more

Solar System, Planets, Moons, Asteroid Belt,Kuiper Belt and Oort Cloud, Comets and Meteoroids

-
Image
 The solar system consists of the Sun, which is a star at its center, and all the celestial bodies bound by its gravitational pull. These bodies include planets, moons, asteroids, comets, and other objects. Key Components of the Solar System: The Sun : The Sun is the center of the solar system and contains about 99.86% of its mass. It is a star primarily composed of hydrogen and helium, providing the heat and light that sustains life on Earth. Planets : There are eight recognized planets in the solar system: Mercury : The closest planet to the Sun, known for extreme temperature variations and no atmosphere. Venus : Similar in size to Earth but with a thick, toxic atmosphere and surface temperatures hot enough to melt lead. Earth : The third planet from the Sun, the only known planet to support life, with water and a breathable atmosphere. Mars : Known as the Red Planet, it has a cold, dry surface and signs of past water. Jupiter : The largest planet, a gas giant, w...
Read more