Question #182074

Write the following statements in symbolic forms.

a.It is cold and it is windy

b. If berries are ripe along the trail, hiking is safe if and only grizzly bears have not been seen in the area.

C. It is necessary to wash the boss's car to get promoted.

d. Winds from the south imply a spring thaw.

e.If you watch television,your mind will decay, and vice versa.

f.Low humidity and sunshine are sufficient for me to play tennis the afternoon.

g.It is snowing but, we will go out for a work.


1
Expert's answer
2021-05-02T08:29:13-0400

(a) Let PP is "it is cold" and QQ is "it is windy", then



It is cold and it is windy(PQ)\text{It is cold and it is windy}\longleftrightarrow\boxed{\left(P\land Q\right)}



(b) Let PP is "berries are ripe along the trail, hiking is safe" and QQ is "grizzly bears have not been seen in the area", then



If berries are ripe along the trail, hiking is safeif and only grizzly bears have not been seen in the area(PQ)\text{If berries are ripe along the trail, hiking is safe}\\[0.3cm] \text{if and only grizzly bears have not been seen in the area}\longleftrightarrow\\[0.3cm] \boxed{\left(P\backsim Q\right)}


(c) Let PP is "to wash the boss's car" and QQ is "to get promoted", then



It is necessary to wash the boss’s car to get promoted(PQ)\text{It is necessary to wash the boss's car to get promoted}\longleftrightarrow\\[0.3cm] \boxed{\left(P\to Q\right)}

(d) Let PP is "a spring thaw" and QQ is "Winds from the south", then



Winds from the south imply a spring thaw(PQ)\text{Winds from the south imply a spring thaw}\longleftrightarrow\boxed{\left(P\to Q\right)}

(e) Let PP is "you watch television" and QQ is "your mind will decay", then



If you watch television, your mind will decay, and vice versa(PQ)\text{If you watch television, your mind will decay, and vice versa}\longleftrightarrow\\[0.3cm] \boxed{\left(P\backsim Q\right)}

(f) Let PP is "low humidity and sunshine" and QQ is "to play tennis the afternoon", then



Low humidity and sunshine are sufficientfor me to play tennis the afternoon(PQ)\text{Low humidity and sunshine are sufficient}\\[0.3cm] \text{for me to play tennis the afternoon}\longleftrightarrow \boxed{\left(P\to Q\right)}

(g) Let PP is "it is snowing" and QQ is "we will go out for work", then



It is snowing but, we will go out for a work(PQ)\text{It is snowing but, we will go out for a work}\longleftrightarrow\\[0.3cm] \boxed{\left(P\land Q\right)}

Q.E.D.

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