Which of the following is true? Option (A) one is an element of the
rational numbers. Option (B) one is not an element of
the rational numbers.
The symbols in this question
represents some formal mathematical notation. The ∊ symbol can be read as an
element of or belongs to or is a member of, and this ℚ symbol represents the set of
rational numbers. So in order to establish if one is
a member of the set of rational numbers or one is not a member of the set of
rational numbers, we’ll need to recall what the rational numbers are.
A rational number is a number which
can be expressed as 𝑝 over 𝑞 where 𝑝 and 𝑞 are integers and 𝑞 is not equal to
zero. We might then look at this number
one and think, “Well, it’s already an integer. How could I express this as a
fraction?” Well, any integer value can be
written as that value over one. Looking at the definition, we can
confirm that the one on the numerator is an integer, and so is the one on the
denominator. And crucially, this number on the
denominator is not equal to zero. This means that one is a member of
the set of rational numbers. Therefore, our answer is that given
in option (A); one is a member of the set of rational numbers.