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
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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:
- hope its correct
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