Which of the following statements are true? (i) \beta(m, n) \in \mathbb{Q} if and only if m,n \in \mathbb{Z^{+}} (ii) \Gamma(n) \in \mathbb{Q} if and only if n \in \mathbb{Z^{+}} (iii) \beta(m, n) = \Gamma(n) if and only if m=n=1 (iv) \beta(\frac{1}{6},\frac{5}{6})=2\pi

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Which of the following statements are true?

(i) $\beta(m, n) \in \mathbb{Q}$ \beta(m, n) \in \mathbb{Q} if and only if $m,n \in \mathbb{Z^{+}}$ m,n \in \mathbb{Z^{+}}

(ii) $\Gamma(n) \in \mathbb{Q}$ \Gamma(n) \in \mathbb{Q} if and only if $n \in \mathbb{Z^{+}}$ n \in \mathbb{Z^{+}}

(iii) $\beta(m, n) = \Gamma(n)$ \beta(m, n) = \Gamma(n) if and only if

m=n=1

(iv) $\beta(\frac{1}{6},\frac{5}{6})=2\pi$ \beta(\frac{1}{6},\frac{5}{6})=2\pi

(ii) and (iii) are correct

33%

(iii) and (iv) are correct

Only (iii) is correct

(ii) and (iv) are correct

❌

(i) and (iii) are correct

Only (iv) is correct

None of the statements are true

All of the statements are correct

33%

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