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Bhagatsinghbiographyintelugupdffree79

Bhagat Singh, revolutionary hero of the Indian independence movement. In 1928 he plotted with others to kill the police chief responsible for the death of Lala .
Bhagat Singh (13 December 1907 – 31 January 1931) was an Indian revolutionary who assassinated British Intelligence Commissioner Harry H.

Early life. Thind was born on October 3, 1892, in the village of Taragarh Talawa of Amritsar district in the state of Punjab in India, .

Bhagat Singh: Revolutionary Leader & Freedom Fighter: Read Kindle Store Reviews – Amazon.com.

Bhagat Singh was a Sikh revolutionary hero of the India independence movement.

The book is a biography in collaboration with the Research Society for Sikhs.

Bhagat Singh, revolutionary hero of the Indian independence movement. In 1928 he plotted with others to kill the police chief responsible for the death of Lala .Q:

For $\lambda\in\mathbb R$, does $\lambda^{ -1}[\mathbb R\setminus\mathbb Q]\subseteq\mathbb R\setminus\mathbb Q$?

This was a question from a recent qualifying exam I had to take, and it was the last question of the first of the two sections. I’ll label the previous three questions as $Q1$, $Q2$, and $Q3$. The solutions were available, so I don’t know if I got the question wrong or if the lecturer simply did not care to answer my question.
So, the question is:

Consider $\lambda\in\mathbb R$, does $\lambda^{ -1}[\mathbb R\setminus\mathbb Q]\subseteq\mathbb R\setminus\mathbb Q$?

The answer for $Q1$ was clearly “Yes” (from one of the hints in the solutions). But I had no idea how to answer the question.
There’s a very simple proof for this question, but I’d like to show that there are other ways to do it.
(Also, I’m not looking for a complete answer to the question; just pointers on the methods that should be used to prove the question.)

A:

Look at this. We have $0<\lambda<1$ and so $0<\lambda<1.$
Now what?

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