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27 votes

What is the correct translation of the following statement into mathematical logic?

“Some real numbers are rational”

- $\exists x (\text{real}(x) \lor \text{rational}(x))$
- $\forall x (\text{real}(x) \to \text{rational}(x))$
- $\exists x (\text{real}(x) \wedge \text{rational}(x))$
- $\exists x (\text{rational}(x) \to \text{real}(x))$

43 votes

Best answer

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Hi @Ayush Upadhyaya sir,

I get confused when to translate a statement as AND (^) and when to use implication (-->) .

eg. None of my friends are perfect... here should i consider Friends ^ Perfect or Friends-->Perfect

For statement : Good mobile phones are not cheap. (from gate 2014) i used implication and that leads to the right answer.

Similarly Not all that glitters is gold(2014) also implication gives the correct result

Any tips or any source to refer pls

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5 votes

“ There exists a number which is real and rational” and this is equal to “Some real number are rational number.”

If possible, can you please draw the ven diagrams for other options given in question ? It might be helpful. @LakshmanPatelRJIT

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Please, check and correct if wrong.

https://gateoverflow.in/?qa=blob&qa_blobid=4820487837657352897

And which tool you used for image ? Don’t know why my image is rotated. :)

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