One odd logical operator.

One odd logical operator. #

Conditional operator p → q is believed to be equivalent of English “if p then q”. It is not. Here is the truth table:

p q p → q
True True True
True False False
False True True
False False True

Truth table makes sense, the only troublesome scenario is when false condition implies truth q in a last row. This just simply means the implication truth is not limited by condition. Consider:
p = “It is raining”
q = “Ground is wet”

p q Statement Result
It is raining Ground is wet If it is raining, then the ground is wet. True
It is raining Ground is not wet If it is raining, then the ground is wet. False
It is not raining Ground is wet If it is not raining, then the ground is wet. True
It is not raining Ground is not wet If it is not raining, then the ground is not wet. True

That is, rainy weather does not eliminate other possibilities of ground being wet. Someone might have spilled some water on the ground.

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