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## Here's the Solution to this Question

(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.