Answer to Question #326010 in Discrete Mathematics for muha

Question

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”.