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Posted: April 14th, 2022
Discrete Mathematics
Q−1: [8×1 marks] Let and be the propositions:
: “Ahmad comes to the party”,
: “Salim comes to the party”,
: “Khalid comes to the party”,
: “Bader comes to the party”.
Write the following propositions using and logical connectives:
a) “Nether Ahmad nor Salim come to the party”.
b) “If Bader comes to the party, then Salim and Khalid come too”.
c) “Khalid comes to the party only if Ahmad and Salim do not come”.
d) “Bader comes to the party if and only if Khalid comes and Ahmad doesn’t come”.
e) “If Bader comes to the party, then, if Khalid doesn’t come then Ahmad comes”.
f) “Khalid comes to the party provided that Bader doesn’t come, but, if Bader comes, then Salim doesn’t come”.
g) “A necessary condition for Ahmad coming to the party is that, if Salim and Khalid aren’t coming, Bader comes”.
h) “Ahmad, Salim and Khalid come to the party if and only if Bader doesn’t come, but, if neither Ahmad nor Salim come, then Bader comes only if Khalid
comes”.
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Q1: [81 points] Let us consider the following propositions:
“Ahmad arrives at the party,”
“Salim arrives at the party,”
“Khalid arrives at the party,”
“Bader arrives at the party.”
Use and logical connectives to write the following propositions:
a) “Neither Ahmad nor Salim show up at the party.”
b) “If Bader comes to the party, Salim and Khalid will also come.”
c) “Khalid will attend the party only if Ahmad and Salim do not.”
d) “Bader attends the party if and only if Khalid attends and Ahmad does not.”
e) “If Bader comes to the party, then Khalid comes, and if Khalid doesn’t come, then Ahmad comes.”
f) “Khalid comes to the party if Bader does not come, but if Bader comes, Salim does not come.”
g) “A must-have”
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