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33 votes
33 votes

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

“Some real numbers are rational”

  1. $\exists x (\text{real}(x) \lor \text{rational}(x))$
  2. $\forall x (\text{real}(x) \to \text{rational}(x))$
  3. $\exists x (\text{real}(x) \wedge \text{rational}(x))$
  4. $\exists x (\text{rational}(x) \to \text{real}(x))$
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4 Answers

Best answer
49 votes
49 votes

Meaning of each choices:

  1. There exists a number which is either real or rational
  2. If a number is real it is rational
  3. There exists a number which is real and rational
  4. There exists a number such that if it is rational, it is real


So, (C) is the answer.

edited by
6 votes
6 votes

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

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4 votes
4 votes
(C) is the answer.

Translation of (C):" There exists a number which is real and rational " and this is eqt to “Some real numbers are rational”.
1 votes
1 votes

short trick

Use ^ for     “there exist(∃)”

use → for     “for ALL”

according to this option c is correct

Answer:

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