Question

Q.1. Transitive property of order of real numbers is that, for all a, b, c belonging to R
Identify the property used in the following:
(a) asb, b<c this implies that a <c
(b) asb, b<c this implies that ac
(c) asb, b<c this implies that a 20
(d) a<b, b<c this implies that ac
0.2. The absolute value of in​

Answer 1

Answer:

Given relation is aRb is 1+ab>0,

Considering both a and b are real numbers,

We know that ab=ba,

⟹aRb=1+ab>0=1+ba>0=bRa,

∴ R is a symmetric relation.

Now, aRa=1+a

2

as a

2

is always a positive real number

∴1+a

2

>0

∴ R is a reflexive relation.

Now consider aRb which implies 1+ab>0 and also bRc which implies 1+bc>0

If we take a=0.5, b=−0.5 and c=−4, then

1+(0.5)(−0.5)=0.75>0 and 1+(−0.5)(−4)=3>

⇒ Both aRb and bRc are satisfied

But, aRc=1+(0.5)(−4)=−2<0

∴ aRc is not a relation

Hence R is not a equivalence relation, but is a reflexive and symmetric relation.

Step-by-step explanation:

1. hope its correct