Answer to Question #262182 in Discrete Mathematics for Abhi

Question

  Consider the following English statements and express as a logical expression with the same meaning. 

The domain is the set of all students at Hogwarts.  

H(x): x is a member of the Hufflepuff.

R(x): x is a member of Ravenclaw.           

T(x,y): x takes a class with y.

a.     There exists a student at Hogwarts

b.     Every student is taking a class with Harry Potter

c.     No student was placed in Hufflepuff

d.     If a student took a class with Ron Weasley, then they did not take one with Harry Potter.

e.     At least one student in Hufflepuff took a class with a student in Ravenclaw

 Two students in Hufflepuff took a class with the same Ravenclaw student

Answer 1

a.

$\exists x$

b.

y is Harry Potter

$\forall xT(x,y)$

c.

$\forall x \neg H(x)$

d.

y₁ is  Ron Weasley, y₂ is Harry Potter

$T(x,y_1)\to \neg T(x,y_2)$

e.

$\exists xT(H(x),R(y))$

$T(H(2x),R(y))$