Written Assignment 1 for Discreet Math

Written Assignment 1

Section 1.1

4. Let p and q be 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.

b): “I bought a lottery ticket this week or I won the million dollar jackpot on Friday.”

e): “I won the million dollar jackpot on Friday if and only if I bought a lottery ticket this week.” Alternative statements of above are: “I bought a lottery ticket this week if and only if I won the million dollar jackpot on Friday.” or “I would have won the million dollar jackpot on Friday if I had bought a lottery ticket this week.”

f): “If I didn’t buy a lottery ticket this week then I didn’t win the million dollar jackpot on Friday.”

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.

f): “You have the flu and miss the final examination or you don’t miss the final examination and pass the course.”

14. Determine whether each of these conditional statements is true or false.

a) If 1+1=3, then unicorns exist. This statement is true. When the premise is false the statement is true, regardless of the truth value of the conclusion.

b) If 1+1=3, then dogs can fly. This statement is true. When the premise is false the statement is true, regardless of the truth value of the conclusion.

c) If 1 + 1 = 2, then dogs can fly. This statement is false. The premise is true but the conclusion is false.

d) If 2+2=4, then 1+2=3. This statement is true. Both the premise and conclusion are true.

28. Construct a truth table for each of these compound propositions.

a)

| | |

T | F | F |

F | T | T |

e)

| | | | | |

T | T | F | F | T | F |

T | F | F | T | F | F |

F | T | T | T | F | F |

F | F | T | T | T | T |

30. Construct a truth table for each of these compound propositions.

e)

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