foundations:logic and Proofs 2. Which of these are propositions? What are the truth values of those that are propositions? a) Do not pass go. b) What time is it? c) There are no black flies in Maine. d)4+x=5. e) The moon is made of green cheese. f)2 n≥100. 4. Let p and qbe the propositions p:I bought a lottery ticket this week. q:I won the million dollar jackpot on Friday. Express each of these propositions as an English sentence. 6. Let p and q be the propositions "The election is decided" and "The votes have been counted," respectively. Express each of pound propositions as an English sentence. 8. Let p, q, and r be the propositions p: You have the flu. q: You miss the final examination. r: You pass the course. Express each of these propositions as an English sentence. 12. Determine whether these biconditionals are true or false. a)2+2=4 if and only if1+1= 2. b)1+1=2 if and only if2 +3= 4. c)1+1=3 if and only if monkeys can fly. d)0>1 if and only if2 > 1. 30. Construct a truth table for each of pound propositions. 32. Construct a truth table for each of pound propositions. 4. Use truth tables to verify the associative laws 10. Show that each of these conditional statements isa tautology by using truth tables. 14. Determine whether tautology. 28. Show that are logically equivalent. 30. Show that isa tautology. 60. Which of pound propositions are satisfiable?
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