Question

Empty relation is the relation R in X given by R = X x X​

Answer 1

Answer:

Let the numbers be a, b and their A.M., G.M., and H.M. be denoted by

A,G, and H respectively. Also we know that A.G.H are in G.P.

or G

2

=AH ...(1)

Since A−G=15 and A−H=27

(A−15)

2

=G

2

=AH by (1) =A(A-27)

or −30A+225=−27Aor3A=225

∴A=75=

2

a+b

∴a+b=150 ...(2)

Since A−G=15∴75−G=15

or G=60=

ab

ab=3600...(3)

Hence from (2) and (3) we conclude that a and b are the roots of t

2

−150t+3600=0

or (t−120)(t−30)=0∴t=120,30

Hence the two numbers are 120 and 30.

Answer 2

SOLUTION

TO DETERMINE

Empty relation is the relation R in X given by

EVALUATION

RELATION

Let S and T be two non empty sets. A binary relation R between S and T is a subset of S × T. If the ordered pair (s, t) ∈ R then the element s of the set S is said to be related to t of the set T by the relation R

EVALUATION

Let X be a non empty set. A binary relation R on X is subset of the Cartesian product X × X

EMPTY RELATION

A relation R in a set X is called empty relation, if no element of C is related to any element of X by the relation R

For example

Let X = Set of all odd integers and

R = { ( a, b) ∈ X × X : a + b is odd }

Then no two elements of X are related by the relation R

$\sf{Here \: \: R = \Phi}$

R is a empty relation on X

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