Answer to Question #185752 in Discrete Mathematics for moses anim

Question

Express the following using language of Predicate Calculus, where it is understood that the people being discussed are in the courtroom. If any sentence is ambiguous, give all symbolic versions. (i) All judges are sober (ii) There is a dishonest lawyer. (iii) All defendants are innocent. (iv) Some plaintiffs are lawyers (v) Anybody who is honest and a defendant is innocent (vi) All defendants who are not sober are dishonest. 

Answer 1

Let A deonte judges

B denote sobers

C denotes honest lawyer

D denotes defendants

E denote Plantiffs

F denote innocent person

G denotes honest persn

(i) All judges are sober

i.e. All A are B

Symbolic representation- $\forall A\to B$

(ii) There is a dishonest lawyer.

i.e. There exist a dishonest C.

Symbolic representation- $\exist (\lnot G\land C)$

(iii) All defendants are innocent.

i.e. All D are F

Symbolic representation- $\forall D\to F$

(iv) Some plaintiffs are lawyers

i.e. some E are C

symbolic representation- $\exist (E\to C)$

(v) Anybody who is honest and a defendant is innocent

i.e. Anybody Who is G and D is F

Symbolic representation- $\forall (G\land D)\to F$

(vi) All defendants who are not sober are dishonest

i.e. All D who are not B are dishonest

Symbolic representation- $\forall (D\cup \lnot B)\to \lnot G$