Problem 1 (a) Let x denote a student, S(x) denote that x is a student of Discret

Question

Problem 1

(a) Let x denote a student, S(x) denote that x is a student of Discrete Structures, C(x) denote x is Chinese, F(x) denote x is French, SF(x) denote x speaks French, and SC(x) mean x speaks Chinese. Then express the following sentences in Predicate Logic: In the Discrete Structures class, some Chinese students speak French, but no French student speaks Chinese.

(b) Let L(x) denote x won the lottery, and P(x) denote x joins the party. Then express the following sentence in Predicate logic: If anyone wins the lottery then everyone joins the party.

(c) Let the predicate M(y) denote “y is a math course”, A(x) denote “x is a part-time student”, and T(x, y) denote “student x is taking course y”. Then write the following statement using these predicated and the necessary quantifiers. There is a part-time student who is not taking any math course.

(d) Assume that the universe for x is all people and the universe for y is the set of all movies. Also, let S(x, y) denote “x saw y” L(x, y) denote “x liked y” A(y) denote “y won an award” and C(y) denote “y is a comedy.” Then write the English statement using the following predicates and any needed quantifiers: (i) No comedy won an award (ii) Some people have seen every comedy

Explanation / Answer

a)

Here x denote a student,

S(x) denote that x is a student of Discrete Structures,

C(x) denote x is Chinese

F(x) denote x is French,

SF(x) denote x speaks French, and

SC(x) mean x speaks Chinese

x y (C(x)^SF(x)^(¬F(y)^SC(y)))

b)L(x) denote x won the lottery,

     P(x) denote x joins the party

     x(L(x)^P(x))

c)M(y) denote y is a math course

A(x) denote x is a part-time student

T(x, y) denote student x is taking course y

x y (A(x)^M(y))^(T(x,y)))

d)Here

x is all people and the universe for y is the set of all movies

S(x, y) denote “x saw y”

L(x, y) denote “x liked y”

A(y) denote “y won an award” and

C(y) denote “y is a comedy.”

      i) y(C(y)^¬A(y))          

ii) x y (C(y)^(S(x,y)))         

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