Questions
A relation R on the set of complex numbers defined by
a
R is reflexive
b
R is symmetric
c
R is transitive
d
R is not equivalence
detailed solution
Correct option is D
Z1RZ1⇒Z1−Z1Z1+Z1=0∴R is Reflexive because 0 is real. Z1RZ2⇒Z1−Z2Z1+Z2 is real ⇒−Z1−Z2Z1+Z2 is real ∴ R is symmetric Z1=a1+ib1; Z2=a2+ib2Z1RZ2⇒Z1−Z2Z1+Z2 is real ⇒a1+a2b1−b2−a1−a2b1+b2=0⇒2a2b1−2b2a1=0⇒a1b1=a2b2∴Z2RZ3⇒a2b2=a3b3therefore a1b1=a3b3∴ Z1RZ3⇒R is transitive.Talk to our academic expert!
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