Negation
The negation is a logical connective that establishes a “not” relationship. Unlike the other connectives that we have covered so far, the negation is unary, meaning it operates on a single statement.
¬a
Although we already somewhat covered the negation in “Everything is Bool”, we will briefly revisit it here.
To negate a statement means to “flip” its boolean value. Similar to a light-switch that turns the light on and off, a negation flips the boolean value of a statement.
A
The above statement states that A, whatever A stands for, is true.
¬A
The above statement states that A is false, and thus, ¬A or “not A” is true.
¬¬A
Furthermore, the above statement states that “not not A” is true. Returning to the light-switch example, if you flipped the switch twice, you return to the original position: one negation means A is false, two negations means A is true (this is the “double negation” rule of inference).
In general, dealing with negations is fairly straightforward, but as the statements we deal with become more complex, it may become a little trickier, so here is an example that applies our last lesson on the “Biconditional”:
Given:
A ↔ ¬B
What is the truth value of B if A is true?
The biconditional tells us that A is true if and only if not B is true. So, B is false.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to
the first studycard and the first level of all activities for free. Get the
app now:
The negation is a logical connective that establishes a “not” relationship. Unlike the other connectives that we have covered so far, the negation is unary, meaning it operates on a single statement.
¬a
Although we already somewhat covered the negation in “Everything is Bool”, we will briefly revisit it here.
To negate a statement means to “flip” its boolean value. Similar to a light-switch that turns the light on and off, a negation flips the boolean value of a statement.
A
The above statement states that A, whatever A stands for, is true.
¬A
The above statement states that A is false, and thus, ¬A or “not A” is true.
¬¬A
Furthermore, the above statement states that “not not A” is true. Returning to the light-switch example, if you flipped the switch twice, you return to the original position: one negation means A is false, two negations means A is true (this is the “double negation” rule of inference).
In general, dealing with negations is fairly straightforward, but as the statements we deal with become more complex, it may become a little trickier, so here is an example that applies our last lesson on the “Biconditional”:
Given:
A ↔ ¬B
What is the truth value of B if A is true?
The biconditional tells us that A is true if and only if not B is true. So, B is false.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: