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Let p and q be the propositions
p : I bought a lottery ticket this week.
q : I won the million dollar jackpot.
Express each of these propositions as an English sentence.

  1. $\neg p$
  2. $p \vee q$
  3. $p \rightarrow q$
  4. $p \wedge q$
  5. $p \leftrightarrow q$
  6. $\neg p \rightarrow \neg q$
  7. $\neg p \wedge \neg q$
  8. $\neg p \vee (p \wedge q)$
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1 Answer

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6 votes

$1.$ I did not buy a lottery ticket this week.

$2.$ Either I bought a lottery ticket this week or won the million dollar jackpot or both

$(or)$

I bought a lottery ticket this week or won the million dollar jackpot or both . 

https://math.stackexchange.com/questions/2130327/does-either-make-an-exclusive-or

$3.$ If I bought a lottery ticket this week then I won the million dollar jackpot.

$4.$ I bought a lottery ticket this week and won the million dollar jackpot.

$5.$ I bought a lottery ticket this week if and only if I won the million dollar jackpot.

$6.$ If I did not buy a lottery ticket this week then I did not win the million dollar jackpot.

$7.$ I did not buy a lottery ticket this week and I did not win the million dollar jackpot .

$8.$ I did not buy a lottery ticket this week or I bought a lottery ticket this week and won the million dollar jackpot .

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