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If $Y=\{1,2,3, \ldots, 10\}$ and $a$ represents any element of $Y$, write the following sets, containing all the elements satisfying the given conditions.
(i) $a \in Y$ but $a^2 \notin Y$
(ii) $a+1=6, a \in Y$
(iii) $a$ is less than 6 and $a \in Y$
(i) $a \in Y$ but $a^2 \notin Y$
(ii) $a+1=6, a \in Y$
(iii) $a$ is less than 6 and $a \in Y$
Solution:
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Verified Answer
We have $Y=\{1,2,3, \ldots, 10\}$
(i) $\quad\left\{a: a \in Y\right.$ and $\left.a^2 \notin Y\right\}=\{4,5,6,7,8,9,10\}$
(ii) $\{a: a+1=6, a \in Y\}=\{5\}$
(iii) $\{$ is less than 6 and $a \in Y\}=\{1,2,3,4,5\}$
(i) $\quad\left\{a: a \in Y\right.$ and $\left.a^2 \notin Y\right\}=\{4,5,6,7,8,9,10\}$
(ii) $\{a: a+1=6, a \in Y\}=\{5\}$
(iii) $\{$ is less than 6 and $a \in Y\}=\{1,2,3,4,5\}$
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