Answer to Question #217540 in Discrete Mathematics for lio

Question

: Let p and q be the propositions.                                                        

p:  “I bought a lottery ticket.”

q:    “I won the million dollar jackpot on Friday.”  

Express each of these propositions as an English sentence.

a) ￢p                        b) ￢p →￢q

c)   p ↔q                     d) ￢p ∨(p ˄ q)

Answer 1

a) The proposition ￢p  is expressed as "I did not buy a lottery ticket".                   

b) The proposition ￢p →￢q is expressed as "If I did not buy a lottery ticket, then I did not win the million dollar jackpot on Friday".

c)  The proposition p ↔q   is expressed as "I bought a lottery ticket if and only if I won the million dollar jackpot on Friday."                  

d)  The proposition ￢p ∨(p ˄ q) is expressed as "I did not buy a lottery ticket or I bought a lottery ticket and I won the million dollar jackpot on Friday".