Answer to Question #172582 in Discrete Mathematics for Vince Reynard D. Simbajon

Question

1. 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.

a) ¬p 

b) p ∨ q 

c) p → q

d) p ∧ q 

e) p ↔ q 

f ) ¬p → ¬q

g) ¬p ∧ ¬q 

h) ¬p ∨ (p ∧ q)

Answer 1

A.) I did not buy a lottery ticket this week.

Negation of p

2

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

Disjunction of p and q

3

C.) If I bought a lottery ticket this week, then I won the million dollar jackpot.

If, then statement

4

D.) I bought a lottery ticket this week and I won the million dollar jackpot.

Conjunction of p and q

5

E.) I bought a lottery ticket this week if and only if i won the million dollar jackpot.

Biconditional Statement

6

F.) If I did not buy a lottery ticket this week, then I will not win the million dollar jackpot.

An if, then statement and negate p and q

7

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

Conjunction and p and q are negated

8

H.) I did not buy a lottery ticket this week and I bought a lottery ticket this week or I did not win the million dollar jackpot.

Negation of p then a conjunction. Then p disjunction of negative q