(a) Let P is "it is cold" and Q is "it is windy", then
It is cold and it is windy⟷(P∧Q)
(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
If berries are ripe along the trail, hiking is safeif and only grizzly bears have not been seen in the area⟷(P∽Q)
(c) Let P is "to wash the boss's car" and Q is "to get promoted", then
It is necessary to wash the boss’s car to get promoted⟷(P→Q)
(d) Let P is "a spring thaw" and Q is "Winds from the south", then
Winds from the south imply a spring thaw⟷(P→Q)
(e) Let P is "you watch television" and Q is "your mind will decay", then
If you watch television, your mind will decay, and vice versa⟷(P∽Q)
(f) Let P is "low humidity and sunshine" and Q is "to play tennis the afternoon", then
Low humidity and sunshine are sufficientfor me to play tennis the afternoon⟷(P→Q)
(g) Let P is "it is snowing" and Q is "we will go out for work", then
It is snowing but, we will go out for a work⟷(P∧Q)
Q.E.D.
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