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Home » State which of the following statements are true and which are false. Justify your answer. (i) 35 ∈ {x | x has exactly four positive factors}. (ii) 128 ∈ {y | the sum of all the positive factors of y is 2y}
State which of the following statements are true and which are false. Justify your answer. (i) 35 ∈ {x | x has exactly four positive factors}. (ii) 128 ∈ {y | the sum of all the positive factors of y is 2y}
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
State which of the following statements are true and which are false. Justify your answer. (i) 35 ∈ {x | x has exactly four positive factors}. (ii) 128 ∈ {y | the sum of all the positive factors of y is 2y}

Solution:

(i) The statement is true

As per the question,

35 \in\{x \mid x has exactly four positive factors \}

1, 5, 7, 35 are the possible positive factors of 35

So, 35 belongs to provided set

As, 35 has exactly four positive factors

\Rightarrow The provided statement 35 \in\{x \mid x has exactly four positive factors \} is true.

(ii) The statement is false

As per the question,

128 \in\{y \mid the sum of all the positive factors of y is 2 y\}

1,2,4,8,16,32,64,128 are the possible positive factors of 128.

Their sum is

\begin{array}{l} =1+2+4+8+16+32+64+128 \\ =255 \\ 2 y=2 \times 128=256 \end{array}

As, the sum of all the positive factors of y is not equal to 2 y

So, 128 does not belong to provided set

\Rightarrow The provided statement 128 \in\{y \mid the sum of all the positive factors of y is 2 y\} is false.

i

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