COMP 047 – Discrete Mathematics HW # 1 just answer the questions the quality should be good and answer the questions specific. COMP 047 – Discrete Mathemat

COMP 047 – Discrete Mathematics HW # 1 just answer the questions the quality should be good and answer the questions specific. COMP 047 – Discrete Mathematics
Homework #1
1) Using a truth table show that the following statements.
a. (p ∧ q) ∨ ~p
b. ~q →(~p ∨ q)
c. (p ∨q)∧(¬p ∨r) →(q ∨r)
d. p∧(q ∨r) ≡ (p∧q)∨(p∧r)
2) Let p and q be the propositions
p : I bought a lottery ticket this week.
q : I won the million dollar jackpot on Friday.
Expression each of these propositions as an English sentence.
a. p ↔ q
b. ¬p → ¬q
3) State the converse, contrapositive, and inverse of each of these conditional statements.
a. If it snows tonight, then I will stay at home.
b. I go to the beach whenever it is a sunny summer day.
c. When I stay up late, it is necessary that I sleep until noon.
4) Express each of these statements using logical operators, predicates, and quantifiers
a. If anyone cheats, everyone suffers.
b. No one talks.
c. Everyone walks or talks.
5) Word Problem
a. Inspector D interviews 3 people, A, B and C. All of them give 2 statements, where 1
statement they say is true and 1 is wrong. The inspector knows that and he also knows
that exactly one is guilty. Here are the statements:
A: It wasn’t me. B did it.
B: It wasn’t me. I know that C did it.
C: It wasn’t me. B does not know who did it.
Who is guilty? Explain your reasoning.

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