2. Consider the following propositions: D is the proposition “You are a dog." C is the proposition “You are a cat." B is the proposition “You love bacon." F is the proposition “You love fish." Write the following propositions using the above: (a) If you are a dog then you love bacon. (b) If you love bacon then you are a dog. (c) If you do not love fish then you are not a cat.

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For the following Boolean functions, give a tabular representation of their Boolean expressions: b) (i) F(x,y, 2) = [X ·y] z 3/7 - (ii) F(x, y, z) = [x ·z] ly z] (iii) What can you say about (i) and (ii) above?

Consider the following propositions: F is the proposition "You are a fish." S is the proposition "You like to swim." W is the proposition "You drink water." H is the proposition "You are human." Write the following propositions symbolically using the above variables: (a) If you are human then you like to swim. (b) If you like to swim then you are a fish. 1 (c) If you do not like to swim then you do not drink water. (d) If you are a human then either you are a fish or you drink water. (e) You are a fish, you do not drink water, and you like to swim.

Translate the following English statements to propositions. 1 It is sunny. 2 I answered the assignment, but I did not submit it. 3 | will remember to send you my address only if you send me an email message. 4 Either I go to school or I go to the mall. 5 I will eat breakfast or I will walk to school, or both.

Postulate: If it rains the sidewalk will be wet. Observation: the sidewalk is wet. From this, we can deduce which of the following: a. Nothing b. No answer text provided. c. No answer text provided. d. It rained

Problem 4)  Translate the given statement into propositional logic using the propositions provided. (Do not simplify the expressions.) “It is not true that you can go out without a hat only if it is warm and not rainy.” Express your answer in terms ofh: “You can go out without a hat”, w: “It is warm”, andr: “It is rainy”.

Write propositional formulas for the following propositions: • s denote “Yida studies"; • t denote “"Steve studies"; • p denote “Yida passes the class"; • q denote “Steve passes the class". d) Both Yida and Steve pass the class but only one of them studies.

For each of the following statements, determine whether they are true or false. If false, write their logical negation (distributing the ¬ across any expressions as necessary) and explain how this negation is true. In each of these, x and y are assumed to be integers. (a) (∀x)(∀y)((y > x) ⇒ (x = 0)) (b) (∃x)(∀y)((y > x) ⇒ (x = 0)) (c) (∀x)(∃y)((y > x) ⇒ (x = 0)) (d) (∀x)(((∀y)(y > x)) ⇒ (x = 0))

The narrator of "The Yellow Wallpaper" agrees to stay in the old house, even though s her husband says it's best for her. What can the reader reasonably infer from this abo a)That she is confused about what her husband is asking of her b)That she is secretly planning her escape from the house, C)• That she is used to following her husband's directions, d) That she often stands up for herself against her husband e) That she is very sick and really does need the rest.