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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM - Grand Test -Q19


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+1 vote

F_1 = \forall a\forall b\exists c (a+b = c)

F_2 = \exists a\forall b\exists c (a+b = c)

F_3 = \forall a\exists b\forall c (a+b = c)

Where domain of a, b, c are Real numbers. Which of the following is true?

(A) Only F_3

(B) Only F_1, F_2

(C) None

(D) All

asked Aug 30, 2020 by gbeditor-2 (72,840 points)
reshown Aug 31, 2020 by gbeditor-2

2 Answers

0 votes
 
Best answer

So, Option B is Correct. 

answered Sep 7, 2020 by deepak-gatebook (226,240 points)
0 votes
F1 can be interpreted as , if you take any pair (a,b) and sum it up to get c = a+b , whether c is a real number or not , which is true.

F2 has a solution space which is subset of F1 , so if F1 is true , F2 is implicitly true.

F3 make the function sum as one to many relation, but one to many relations are not functions , thus F3 is inherently False.

Thus B should be the correct choice.
answered Sep 6, 2020 by prashantpro19 (970 points)
F1, F2, F3 are Not functions But first order logic formulas.
Obviously they are FOL formulas , I interpreted them like that , because in this case they can be interpreted like that . But as far as Logic is concerned , I guess I needed to add more with the explanation .
Answer:

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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