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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: $\dpi{100} \exists x (T(x)\land \sim C(x))$

2. Some tool is not in the correct place: $\dpi{100} \exists x (\sim C(x))$

3. All tools are in the correct place and are in excellent condition: $\dpi{100} \forall x(T(x)\rightarrow (C(x)\land E(x)))$.

4. All tools are in the correct place and are in excellent condtion: $\dpi{100} \forall x(C(x)\land E(x))$.

Which of the above is/are Correct?

(A) Only 1 and 3

(B) Only 2 and 4

(C) All

(D) None

reshown Aug 31, 2020

+1 vote

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 (226,240 points)
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.