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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

asked Aug 30, 2020
reshown Aug 31, 2020

## 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 (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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