- 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"
- Samantha is not smart but her GPA is 3.8.
- Samantha is neither healthy, wealthy, nor smart.
- If Samantha does her homework on her own then she passes CSC 201.
- Samantha passes CSC 201 only if she does her homework on her own.
- Passing CSC 201 is a sufficient condition for Samantha to do her homework.
- Answer the following questions. There is no partial credit for this problem.
- Write the inverse of "If you do not feel well, then you should not go to work" informally (in ENGLISH).
- Write the negation of "If you do not feel well, then you should not go to work" informally (in ENGLISH).
- Write the negation of "k is zero or k is positive" informally (in ENGLISH).
- Rewrite the following statements formally using predicate variables and the symbols "/$.
- No airplanes are small.
- Some rational numbers are nonzero.
- 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
- Define statement variables (e.g., p, q) and rewrite the above argument into an argument form.
- Is the above argument form valid? Why? Do not use a truth table when justifying your answer.
- 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.
- 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
- Perform the following arithmetic. You need to show all of your work.
- 8AEC16 + 235F16
- 502.48 - 177.58
- 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.
- p -> q
- r s
- ~q s
- ~s
- ~p r -> u
u
- [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