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3. Let p and q be the propositions. p : I bought a lottery ticket this week. q : I won the million-dollar jackpot on

3. Letpandqbe the propositions.

p: I bought a lottery ticket this week.

q: I won the million-dollar jackpot on Friday.

I bought a lottery ticket this week and I won the million-dollar jackpot on Friday.

Express of each of these propositions as an English sentence:

a) ~p

b) p^q

c) p v q

d) (~p) ^ (~q)

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