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GO Classes CS/DA 2025 | Weekly Quiz 2 | Fundamental Course | Question: 5

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Consider the following statements:

  • $\text{S1}:$ Given any $x \in \mathbb{R}$, there exists an element $y \in \mathbb{R}$ for which $x y=1$.
  • $\text{S2}:$ There exists two irrational numbers $x$ and $y$ such that $x+y$ is rational.

Which of the above statements is true?

  1. Only $\text{S1}$
  2. Only $\text{S2}$
  3. Both $\text{S1}\; \&\; \text{S2}$
  4. None
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$\text{S2}$ is a GATE question: https://gateoverflow.in/720/gate-cse-2001-question-2-2

Video Solution of $S2:$ https://youtu.be/elIjrJmtvq4?t=189 

$\text{S1}:$ Given any $x \in \mathbb{R}$, there exists an element $y \in \mathbb{R}$ for which $x y=1$.

It's FALSE, because given $x=0 \in \mathbb{R}$, there does not exist any real number $y$ for which $x y=1$.

Detailed Video Solution - Weekly Quiz 2

Annotated Notes - Weekly Quiz 2 Solutions 

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