Midterm 1

The proposition  (p →q ) ↔ (q → p) is:

• A tautology

• A contradiction

• Neither tautology or contradiction

Which of the following is the contrapositive of the following statement:

If there are two feet of snow on the ground, class is canceled.

• If class is not canceled, there aren't two feet of snow on the ground.

•  

  If class is canceled, there are two feet of snow on the ground.

• If there aren't two feet of snow on the ground, class won't be canceled.

x     y     (x → y) ↔ (¬x ∨ y)

F    F                

F    T                

T    F              

T    T    

• T, T, T, T

• T, F, T, F

• F, T, F, T

• F, F, F, F

Which statement is incorrect?

• The biconditional p ↔ q means “if p then q and conversely”

• The biconditional p ↔ q is true when p and q have the same truth value

•  

  The biconditional p ↔ q is the same as “if p then q”

• The biconditional p ↔ q is the proposition “p if and only if q”

x     y     (x ↔ y) ⊕ (x ↔ ¬y)

• T, T, T, T

• T, F, T, F

• F, T, F, T

• F, F, F, F

x     y     ¬x → y

• T, F, F, F

• F, T, T, T

• F, F, F, F

• T, T, T, T

The proposition  (p ∧ q ) ∨ (¬p ∧ ¬q) is a:

• Contradiction

•  

  Tautology

•  

  Neither tautology or contradiction

Given the following predicates, which is not equivalent with the others?

• ∀x ¬P(x))

• ∃x ¬P(x)

•  

  ¬(∀x P(x))

Given ¬p, ¬q and r → (p ∨ q), which of the following is true?

•  

  r

•  

  ¬r

Every student in the university has lived in the dorms.  Moses has not lived in the dorms.  Therefore Moses was not a student in the university.

• True

• False