Week 2 - 2 PROPOSITIONAL LOGIC EXAMPLE PART 2

[Music] let's continue our discussion about english translation so let's have this example let p and q be the prepositions p i bought a lottery ticket this week q i won the million dollar jackpot so we're going to express this um the given equation to its equivalent english statement so let's have the first question not p so negation of p so the answer will be i did not buy a lottery ticket this week so we negate the facts about about me about buying a lottery ticket okay next question p or q so basically we're just going

to combine pq with or so the result will be either i bought a lottery ticket this week or i won the million dollar jackpot on friday okay so using the or word to connect the two proposition next question p implies q p is our premise q is our consequence so the result will be if i bought a lottery ticket this week comma then i won the million dollar jackpot on friday okay next question pntu so we're going to have a compound proposition using ant so we're going to connect pq with ant weight so the result

will be i bought a lottery ticket this week and i won the million dollar jackpot on friday okay next question p by going by conditional q so the english statement is i bought a lottery ticket this week if and only if i won the million dollar jackpot on friday okay next not b implies not q so the premise and consequence are repeated so the result will be if i did not buy a lottery ticket this week comma then i did not win the million dollar jackpot on friday okay so we decayed the predicate of each

propositions [Music] x not p and not q so the result would be i did not buy a lottery ticket this week and i did not buy i did not win the million dollar jackpot on friday okay last not p or two p and q okay so first about or either i did not buy a lottery ticket this week for nappy or or else i did buy one and won the million dollar jackpot on friday for pnk okay so that's how we transform a mathematical mathematical equation to its equivalent english sentence okay so more example and

further discussion of logic logic will be discussed on the next feature lecture thank you [Music] you