Reference no: EM13161048

1. Write the following statements IN SYMBOLIC FORM using the symbols (e.g., ~, , , ? , ?). The indicated letters represent propositions. There is no partial credit for this problem.

 

      h = "Samantha is healthy"

      w = "Samantha is wealthy"

      b = "Samantha is smart"

      g = "Samantha's GPA is not 3.8"

      d = "Samantha does her homework on her own"

      p = "Samantha passes CSC 201"

1.  Samantha is not smart but her GPA is 3.8.

1.  Samantha is neither healthy, wealthy, nor smart.

1.  If Samantha does her homework on her own then she passes CSC 201.

1.  Samantha passes CSC 201 only if she does her homework on her own.

1.  Passing CSC 201 is a sufficient condition for Samantha to do her homework.

1. Answer the following questions. There is no partial credit for this problem.

 

1.  Write the inverse of "If you do not feel well, then you should not go to work" informally (in ENGLISH).

1.  Write the negation of "If you do not feel well, then you should not go to work" informally (in ENGLISH).

1.  Write the negation of "k is zero or k is positive" informally (in ENGLISH).

1. Rewrite the following statements formally using predicate variables and the symbols "/$.

1.  No airplanes are small.

1.  Some rational numbers are nonzero.

1. Answer the questions for the following argument.
   • If at least one of these two numbers is divisible by 10, then the product of these two numbers is divisible by 10
   • Neither of these two numbers is divisible by 10
   • Therefore, the product of these two numbers is not divisible by 10

 

1.  Define statement variables (e.g., p, q) and rewrite the above argument into an argument form.

1.  Is the above argument form valid? Why? Do not use a truth table when justifying your answer.

1.  Use a truth table to determine whether or not the following argument form is valid. You can justify your answer by doing the following: indicate which columns represent the premises and which represent the conclusion; specify which rows are critical rows. You MUST use the standard order for the truth table.

1.  Find the internal representation of the following decimal number in the Single Precision Floating Point format. Non-terminating fraction should be carried out 6 places. You need to show all of your work and label EVERYTHING for full credit. Your final answer must be in Hexadecimal notation.

            33.6

1. Perform the following arithmetic. You need to show all of your work.

1.  8AEC₁₆                        +          235F₁₆

1.  502.4₈                  -           177.5₈

1.  A set of premises and a conclusion are given below. Use the valid argument forms to deduce the conclusion from the premises, giving a reason for each step. Note that all variables are statement variables.

1. p -> q
2. r s
3. ~q s
4. ~s
5. ~p r -> u

u

1. [10 pts] Use Theorem 2.1.1 to verify the logical equivalences of the following statement forms. You must supply a reason for each step.

 

( p ( ~ ( ~ p q ) ) ) ( p q )               p