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Express these system specifications using the propositions p “The user enters a valid password,” q “Access is granted,” and r “The use
Question
Express these 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 (including negations).
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.”
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Mathematics
5 years
2021-07-26T02:22:57+00:00
2021-07-26T02:22:57+00:00 1 Answers
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Answers ( )
Answer:
a) r ⋀~p
b)(r⋀p)⟶q
c) ~r ⟶ ~q
d) (~p ⋀r) ⟶q
Step-by-step explanation:
To solve this question we will make use of logic symbols in truth table.
We are told that;
p means “The user enters
a valid password,”
q means “Access is granted,”
r means “The user has paid the
subscription fee”
A) The user has paid the subscription fee, but does not enter a valid
password.”
Fist part of the statement is correct and so it will be “r”. Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is “⋀” Thus, we have; r ⋀~p
B) Still using logic symbols, we have;
(r⋀p)⟶q
⟶ means q is true when r and p are true.
C) correct symbol is ~r ⟶ ~q
Since both statements are negation of the question. And also, if ~r is true then ~q is also true.
D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q