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Question Number 1208 by 123456 last updated on 14/Jul/15

wich statment is true

1 . if x \in Q and y \in Z, then x y \in Q / Z

2 . if x \in Q / Z and y \in Z, then x y \in Q / Z

3 . if x \in R, then \exists y \in R such that x y = 5

4 . if x \in N / {0}, then \exists y \in Q such that \sqrt{\frac{y (x + 2)}{x (x + 1)}} \in Q

Answered by prakash jain last updated on 18/Jul/15

1 . false x = 1, y = 1, x y \notin Q / Z

2 . false . x = \frac{1}{2}, y = 1, x y \notin Q / Z

3 . false . x = 0 ∄ y \in R such that x y = 5

4 . true

\frac{y (x + 2)}{x (x + 1)} = \frac{p^{2}}{q^{2}} \Rightarrow y = \frac{p^{2} x (x + 1)}{q^{2} (x + 2)}, x, p, q \in N \Rightarrow y \in Q