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State whether the following statement is true or false.

If $x$ is a rational number and $y$ is an irrational number, then $x y$ must be also an irrational number.

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True

False

answer is B.

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Detailed Solution

It is given that

x

is a rational number and

y

is an irrational number.
We know that rational numbers are represented in

p q

form wherein q isn't equal to 0. It is likewise a kind of real number.
Hence, we could say that ‘0’ is also a rational number.
Let’s assume

x = 0

and

y

be any irrational number.
Then

x y = 0,

since a product of any number with 0 always results 0.
We know that 0 is a rational number, therefore

x y

is also a rational number.
Thus, if

x

is a rational number and

y

is an irrational number, then

x y

may or may not be an irrational number.
Therefore, the given statement is not true.
Hence, option (2) is correct.

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