Answer to Question #181793 in Discrete Mathematics for Romnick Lucas

Question

Translate the following English sentence into symbol. (3 pts each)

1. No one in this class is wearing pants and a guitarist.

Let:

Domain of x is all persons

A(x): x is wearing pants

B(x): x is a guitarist

C(x): belongs to the class

Answer: __________________________________________________

2. No one in this class is wearing pants and a guitarist.

Let:

Domain of x is persons in this class

A(x): x is wearing pants

B(x): x is a guitarist

Answer: __________________________________________________

3. There is a student at your school who knows C++ but who doesn’t 

know Java.

Let:

Domain: all students at your school

C(x): x knows C++

J(x): x knows Java

Answer: __________________________________________________

Answer 1

1) No one in this class is wearing pants and a guitarist:

Let:

Domain of x is all persons

A(x): x is wearing pants

B(x): x is a guitarist

C(x): belongs to the class

Answer: $\forall x\left( {C(x) \to \overline {A(x) \wedge B(x)} } \right)$

2) No one in this class is wearing pants and a guitarist.

Let:

Domain of x is persons in this class

A(x): x is wearing pants

B(x): x is a guitarist

Answer: $\forall x\left( {\overline {A(x) \wedge B(x)} } \right)$

3) There is a student at your school who knows C++ but who doesn’t 

know Java.

Let:

Domain: all students at your school

C(x): x knows C++

J(x): x knows Java

Answer: $\exists x\left( {C(x) \wedge \overline {J(x)} } \right)$