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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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DM - Grand Test -Q17


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+1 vote

Let C(x) denote the predicate "x is in the correct place", let E(x) denote the predicate "x is in excellent condition", and let T(x) denote the predicate "x is a tool" and suppose that the domain consists of all tools.

Consider the following statements and their equivalent expressions in Predicate calculas:

1. Some tool is not in the correct place: \exists x (T(x)\land \sim C(x))

2. Some tool is not in the correct place: \exists x (\sim C(x))

3. All tools are in the correct place and are in excellent condition: \forall x(T(x)\rightarrow (C(x)\land E(x))).

4. All tools are in the correct place and are in excellent condtion: \forall x(C(x)\land E(x)).

Which of the above is/are Correct?

(A) Only 1 and 3

(B) Only 2 and 4

(C) All

(D) None

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

2 Answers

+1 vote
 
Best answer
Read the information , "suppose that the domain consists of all tools." .
The domain only has tools , so having a predicate T(x) is redundant.

Since the domain is "All tools", so, T(x) is always true, so, it is redundant if it is written.
answered Sep 7, 2020 by deepak-gatebook (226,240 points)
0 votes
in statement 2 and 4  how x can be considered as x is tool without T(x)

 1 and 3 are correct
answered Sep 7, 2020 by (18,750 points)
Hi ,
Read the information , "suppose that the domain consists of all tools." .
The domain only has tools , so having a predicate T(x) is redundant.
Answer:

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