A relation R on the set of complex numbers defined by Z1RZ2⇔Z1-Z2Z1+Z2 is real then which of the following is not true?
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a
R is reflexive
b
R is symmetric
c
R is transitive
d
R is not equivalence
answer is D.
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Detailed Solution
Z1RZ1⇒Z1-Z1Z1+Z1=0∴ R is Reflexivebecause 0 is real. Z1RZ2⇒Z1-Z2Z1+Z2isreal⇒-Z1-Z2Z1+Z2isreal ∴R is symmetric Z1=a1+ib1; Z2=a2+ib2 Z1RZ2⇒Z1-Z2Z1+Z2is realimaginary portion zero⇒a1+a2b1-b2-a1-a2b1+b2=0⇒2a1b2-2b1a2=0⇒a1b1=a2b2 so it is transitivefinally it is equivalance