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.