Screenshot (4).png - Photos 1. Let r be the proposition \"The data is secure\",

Question

Screenshot (4).png - Photos 1. Let r be the proposition "The data is secure", y be the proposition "The computer has a virus". Translate the following expressions into English. 2. Translate the following logical propositions into English expressions. Let a be the proposition "The economy is improving", b be "I make money", c be "I have a job" and d be "I finish my degree at Carleton". (a) (d b) b 3. Translate the following English expressions into logical statements. You must explicitly state what are the atomic propositions and then show their logical relation. (a) If I do exercise then I am in shape and if I am in shape then I do not exercise COMP1805B - W18 Assignment 1 Due Thursday, Jan 25 at noon (b) The sun is bright or it is cloudy. (c) If the road conditions are bad or I am distracted then I have an accident (d) If I can ski then I cannot skate, and, if I cannot ski and I cannot skate, then I do not like winter

Explanation / Answer

1)

Given

x = The data is secure

y = The computer has a virus

a) ¬x y = the data is not secure and computer has a virus

b) x ¬y = if data is secure then computer dont has a virus

c) y xor x = either the computer has a virus or the data is secure.

2)

Given

a = the economy is improving

b = i make money

c = i have a job

d = i finish my degree at carleton

a) (db) b = if i finish my degree at carleton and i make money then i make money

b) ¬b ¬c = if i dont make money then i dont have a job

c) (¬b ¬c) d = if i dont make money and i dont have a job then i finish my degree at carleton

3)

a)

assume

p = i do exercise

q = i am in shape

If i do exercise then i am in shape and if i am in shape then i do not exercise

(pq)(q¬p)

b)

assume

p = the sun is bright

q = the sun is cloudy

the sun is bright or it is cloudy

pq

c)

assume

p = the road conditions are bad

q = i am distracted

r = i have an accident

if the road conditions are bad or i am distracted then i have an accident

(pq)r

d)

assume

p = i can ski

q = i can skate

r = i like winter

If i can ski then i cannot skate and, if i cannot ski and i cannot skate,then i do not like winter

(p¬q)((¬p¬q)¬r)

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