Video: Determining Whether a Number Belongs to a Given Number Set

Which of the following is true? [A] 1 ∈ ℚ [B] 1 ∉ ℚ

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Video Transcript

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.

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