if b²=ac show that a⁴+a²b²+b²/b⁴+b²c²+c⁴=a²/c²
Answers
Correct option is
A
Symmetric but neither reflexive nor transitive
According to the question,
Given set S={....,−2,−2,0,1,2,...}
And R={(a,b):a,b∈S and a
2
+b
2
=1}
Formula:
For a relation R in set A
Reflexive
The relation is reflexive if (a,a)∈R for every a∈A
Symmetric
The relation is Symmetric if (a,b)∈R, then (b,a)∈R
Transitive
Relation is transitive if (a,b)∈R and (b,c)∈R, then (a,c)∈R
Equivalence
If the relation is reflexive, symmetric and transitive, it is an equivalence relation.
Check for reflexive
Consider (a,a)
∴ a
2
+a
2
=1 which is not always true.
If a=2
∴ 2
2
+2
2
=1⇒4+4=1 which is false.
∴ R is not reflexive ---- ( 1 )
Check for symmetric
aRb⇒a
2
+b
2
=1
bRa⇒b
2
+a
2
=1
Both the equation are the same and therefore will always be true.
∴ R is symmetric ---- ( 2 )
Check for transitive
aRb⇒a
2
+b
2
=1
bRc⇒b
2
+c
2
=1
∴ a
2
+c
2
=1 will not always be true.
Let a=−1,b=0 and c=1
∴ (−1)
2
+0
2
=1, 0
2
+1
2
=1 are true.
But (−1)
2
+1
2
=1 is false.
∴ R is not transitive ---- ( 3 )
Now, according to ( 1 ), ( 2 ) and ( 3 )
Correct answer is option A.