Please solve the question given in attachment.
Answers
Answer:
Option (B) is correct
Step-by-step explanation:
In the question we are given that x belongs to set of rational numbers ( denoted by Q ) and y be the set of irrational numbers ( denoted by Q compliment ), we are asked to find the statement which is always incorrect out of the given statements.
It is clear that option (B) is incorrect because irrational divide by rational number is always an irrational number. But the option states that irrational number divide by rational is always rational whenever defined. This contradicts the fact that irrational divide by rational is irrational.
Therefore option (B) is incorrect and hence the correct option.
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Let's also discuss about the other options.
Option (A) :-
According to option ( A ), product of rational number and irrational number is an irrational number.
Well this is quite right but not for all i.e. there exists a rational number which when multiplied by any irrational number results 0. That's nothing but 0. 0 is a rational number which always results 0 when multiplied by anything.
But we have to choose the number which is always correct. Therefore this is not a correct choice for answer.
Option (C) :-
According to this option, √2 x + y is a rational number. This is not true for rational number 0 but is true for rational number = 1 and irrational number = -√2 therefore this option is sometimes correct and sometimes incorrect.
Therefore it's not a correct choice of answer.
Option (D) :-
According to this option, irrational number divided by rational number is an irrational number.
This is true that irrational number divide by rational number is always an irrational number. For ex - √2/6 is always an irrational number.
Since this is a correct option, it's not the correct choice of answer.
Answer:
Option (B) is correct
Step-by-step explanation:
y/x is always irrational whenever defined. Therefore option (B) is incorrect and correct choice of answer.