Problem 8E

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.

Solution:

Step1

Given that

I bought a lottery ticket this week and I won the million dollar jackpot be a preposition p and q.

Step2

To find

Express each of these propositions as an English sentence.

Step3

From the given proposition we are finding that

a.

This means this week i have not buy a lottery ticket.

Step4

b.

This means this week either i bought a lottery ticket or i won the million dollar jackpot.

Step5

c.

This means this week if i bought a lottery ticket then the million dollar jackpot i won.

Step6

d.

This means this week if i bought a lottery ticket and the million dollar jackpot i won.

Step7

e.

This means this week if i bought a lottery ticket if and only if the million dollar jackpot i won.

Step8

f.

This means this week if i have not bought a lottery ticket then the million dollar jackpot i have not won.

Step9

g.

This means this week if i have not bought a lottery ticket and the million dollar jackpot i have not won.

Step10

h.

This means either this week i have not bought a lottery ticket or else i have and the million dollar jackpot i won.