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Home » If Y = {1, 2, 3,…, 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. (i) a ∈ Y but a2∉ Y (ii) a + 1 = 6, a ∈ Y
If Y = {1, 2, 3,…, 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. (i) a ∈ Y but a2∉ Y (ii) a + 1 = 6, a ∈ Y
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
If Y = {1, 2, 3,…, 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. (i) a ∈ Y but a2∉ Y (ii) a + 1 = 6, a ∈ Y

Solution:

(i) As per the question,

Y=\{1,2,3, \ldots, 10\} in which a represents any element of Y

\begin{array}{l} Y=\{1,2,3, \ldots, 10\} \\ 1^{2}=1,2^{2}=4,3^{2}=9 \end{array}

1,4,9 \in Y \Rightarrow 1,2,3 do not satisfy condition given

As a result,

\left\{a: a \in Y\right. and \left.a^{2} \notin Y\right\}=\{4,5,6,7,8,9,10\}

(ii) As per the question,

Y=\{1,2,3, \ldots, 10\} in which a represents any element of Y

\begin{array}{l} Y=\{1,2,3, \ldots, 10\} \\ a+1=6 \Rightarrow a=5 \end{array}

\Rightarrow 5 satisfies the condition given

As a result,

\{a: a+1=6, a \in Y\}=\{5\}

i

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