, so you have false statement.
similar as case a)
I'm teaching myself propositional logic at home and I can't understand the difference between these two statements in the book. I think one of these represents that 'age is not between 65 and 80 inclusive', but I'm really not sure. If someone could explain what each of the statements mean that would be great. Then I can carry on with my reading!!
Here are the two I don't know the difference between:
¬ ((age ≥ 65) ∨ (age ≤ 80))
¬ (age ≥ 65) ∨ ¬ (age ≤ 80)
Thanks in advance!
see DeMorgan's laws on Wikipedia): "age is not at least 65, and age is not at most 80". We can simplify this noting that the inverse of "at least" is "less than", etc.: "age is less than 65, but more than 80". This is a contradiction.
The second one is equivalent to "age is less than 65 or more than 80", which is the opposite of what you want (this is true only when age is not in the range you want).
Just build it by using English. "Age is between 65 and 80 inclusive," becomes "age is at least 65 and age is at most 80". Does that help...?