$\exists x( Real(x) \implies Rational(x) )$

In English: There exists an x such that, if x is real then it is rational.

5,099 views

Best answer

@Pratyush, No that is incorrect because implication is also true when the antecedent is false.

Some numbers might not be real, and since here no domain is specified we consider domain of all numbers be it an integer or real etc.

So, when some number is not real, say it is integer, your first part of implication becomes false and hence the whole implication becomes true which should not happen.

Some numbers might not be real, and since here no domain is specified we consider domain of all numbers be it an integer or real etc.

So, when some number is not real, say it is integer, your first part of implication becomes false and hence the whole implication becomes true which should not happen.

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

“ 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

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. :)

Search GATE Overflow