Posted: April 14th, 2022

Discrete Mathematics

Q−1: [8×1 marks] Let and be the propositions:

: “Ahmad involves the social gathering”,

: “Salim involves the social gathering”,

: “Khalid involves the social gathering”,

: “Bader involves the social gathering”.

Write the next propositions utilizing and logical connectives:

a) “Nether Ahmad nor Salim come to the social gathering”.

b) “If Bader involves the social gathering, then Salim and Khalid come too”.

c) “Khalid involves the social gathering provided that Ahmad and Salim don’t come”.

d) “Bader involves the social gathering if and provided that Khalid comes and Ahmad doesn’t come”.

e) “If Bader involves the social gathering, then, if Khalid doesn’t come then Ahmad comes”.

f) “Khalid involves the social gathering supplied that Bader doesn’t come, however, if Bader comes, then Salim doesn’t come”.

g) “A mandatory situation for Ahmad coming to the social gathering is that, if Salim and Khalid aren’t coming, Bader comes”.

h) “Ahmad, Salim and Khalid come to the social gathering if and provided that Bader doesn’t come, however, if neither Ahmad nor Salim come, then Bader comes provided that Khalid

comes”.

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Q1: [81 points] Allow us to think about the next propositions:

“Ahmad arrives on the social gathering,”

“Salim arrives on the social gathering,”

“Khalid arrives on the social gathering,”

“Bader arrives on the social gathering.”

Use and logical connectives to put in writing the next propositions:

a) “Neither Ahmad nor Salim present up on the social gathering.”

b) “If Bader involves the social gathering, Salim and Khalid will even come.”

c) “Khalid will attend the social gathering provided that Ahmad and Salim don’t.”

d) “Bader attends the social gathering if and provided that Khalid attends and Ahmad doesn’t.”

e) “If Bader involves the social gathering, then Khalid comes, and if Khalid does not come, then Ahmad comes.”

f) “Khalid involves the social gathering if Bader doesn’t come, but when Bader comes, Salim doesn’t come.”

g) “A must have”

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