Implication/Equivalence
p : It is below freezing.
q : It is snowing.
Determine the propositional form of the given sentence with symbols: If it is below freezing, it is also snowing.
p→q
p : It is below freezing.
q : It is snowing.
Determine the propositional form of the given sentence with symbols: It is below freezing but not snowing.
p∧¬ q
b: berries are ripe along the path
r: rabbits have been seen in the area
Determine the propositional form of the given sentence with symbols: Berries are ripe along the path, but rabbits have not been seen in the area.
b∧¬ r
What is a Proposition?
A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.
p: I bought a lottery ticket
q: I won the jackpot
Express the following as a natural English sentence: p ⇒ q
If I bought a lottery ticket, then I won the jackpot
What is another term for implication?
Conditional
What is another term for equivalence?
Bi-Conditional
Free Points
Yay!!!
p: I bought a lottery ticket
q: I won the jackpot
Express the following as a natural English sentence: p ⇒ q
If I bought a lottery ticket, then I won the jackpot.
p: I bought a lottery ticket
q: I won the jackpot
Express the following as a natural English sentence: ¬p∨(p∧q)
Either I did not buy a lottery, or I bought a lottery ticket and won the jackpot.
b: berries are ripe along the path
r: rabbits have been seen in the area
w: walking on the path is safe
Determine the propositional form of the given sentence with symbols: Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
(r∧b) ⇒ ¬ w
b: berries are ripe along the path
r: rabbits have been seen in the area
w: walking on the path is safe
Translate the following to natural English sentences: (¬r∧w)∧b
Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.