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For a person $p$, let $w(p)$, $A(p, y)$, $L(p)$ and $J(p)$ denote that $p$ is a woman, $p$ admires $y$, $p$ is a lawyer and $p$ is a judge respectively. Which of the following is the correct translation in first order logic of the sentence: "All woman who are lawyers admire some judge"?

  1. $\forall x: \left[\left(w\left(x\right)\Lambda L \left(x\right)\right)\Rightarrow \left(\exists y:\left(J \left(y\right)\Lambda w\left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$
  2. $\forall x: \left[\left(w\left(x\right)\Rightarrow L \left(x\right)\right)\Rightarrow \left(\exists y:\left(J \left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$
  3. $\forall x \forall y: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right]$
  4. $\exists y \forall x: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right]$
  5. $\forall x: \left[\left(w\left(x\right) \Lambda L\left(x\right)\right) \Rightarrow \left(\exists y: \left(J\left(y\right) \Lambda A\left(x, y\right)\right)\right)\right]$
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5 Answers

Best answer
41 votes
41 votes

Just translating to English:

  1. Every women who is a lawyer admires some women judge.
  2. If a person being women implies she is a lawyer then she admires some judge. OR If a person is not women or is a lawyer he/she admires some judge.
  3. Every women who is a lawyer admires every judge.
  4. There is some judge who is admired by every women lawyer.
  5. Every women lawyer admire some judge. 

So, option (e) is the answer. 

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3 votes
3 votes

It will be (e).

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1 votes
(e) is the correct translation.
∀x:[(w(x)ΛL(x))⇒(∃y:(J(y)ΛA(x,y)))]  :"For every person x, if x is woman AND lawyer then she admires some judge"  which is equivalent to say "Every women lawyer admire some judge" .

So, Ans is (e).
Answer:

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