Answer to Question #182074 in Discrete Mathematics for nayeem

Question

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.

Answer 1

(a) Let $P$ is "it is cold" and $Q$ is "it is windy", then

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

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

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

(c) Let $P$ is "to wash the boss's car" and $Q$ is "to get promoted", then

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

(d) Let $P$ is "a spring thaw" and $Q$ is "Winds from the south", then

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

(e) Let $P$ is "you watch television" and $Q$ is "your mind will decay", then

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

(f) Let $P$ is "low humidity and sunshine" and $Q$ is "to play tennis the afternoon", then

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

(g) Let $P$ is "it is snowing" and $Q$ is "we will go out for work", then

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

Q.E.D.