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DISCRETE MATH: Express the following using propositions p,q,r and logical connectives

  • Thread starter VinnyCee
  • Start date
489
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1. Homework Statement

Express the system specifications using the propositions p "The user enters a valid password," q "Access is granted," and r "The user has paid the subscription fee" and logical connectives.

a) The user has paid the subscription fee, but does not enter a valid password.

b) Access is granted whenever the user has paid the subscription fee and enters a valid password.

c) Access is denied if the user has not paid the subscription fee.

d) If the user has not entered a valid password but has paid the subscription fee, then access is granted.

2. Homework Equations

p = "The user enters a valid password"
q = "Access is granted"
r = "The user has paid the subscription fee"


3. The Attempt at a Solution

a) [tex]r\,\wedge\,\neg\,p[/tex]

b) [tex]q\,\longleftrightarrow\,(r\,\wedge\,q)[/tex]

c) [tex]\neg\,r\,\longrightarrow\,\neg\,q[/tex]

d) [tex](\neg\,p\,\wedge\,r)\,\longrightarrow\,q[/tex]


Do these answers look right?
 

Answers and Replies

radou
Homework Helper
3,104
6
Everything looks right, except you made a typo (I guess) in b), it should be [tex]q\,\longleftrightarrow\,(r\,\wedge\,p)[/tex], unless I'm missing something.
 
matt grime
Science Advisor
Homework Helper
9,394
3
Even modulo typos, b is not right. The implication is not both ways. It does not assert that the only way to get access is with subscription and a valid password.
 
radou
Homework Helper
3,104
6
Even modulo typos, b is not right. The implication is not both ways. It does not assert that the only way to get access is with subscription and a valid password.
Excuse my mistake, it should be [tex](r \wedge p) \Rightarrow q[/tex].
 
489
0
So they are all right except that B is really [tex](r\,\wedge\,p)\,\longrightarrow\,q[/tex]?
 
radou
Homework Helper
3,104
6
So they are all right except that B is really [tex](r\,\wedge\,p)\,\longrightarrow\,q[/tex]?
Yes, you already have two answers which implied that. :wink:
 

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