Definition
Negation
Negation forms the “not” version of a statement and reverses its truth value.
What it means
Negation flips a statement’s truth value. It must cover every case where the original claim fails. For an inequality, keep the boundary: everything outside x > 5 is included by x ≤ 5; using only x < 5 would miss x = 5.
Remember it
Negation means “not this,” with no missing cases.
Example
Let p be “12 is odd.” The statement p is false, so its negation, “12 is not odd,” is true.
Watch for
The negation of “all shapes are blue” is “at least one shape is not blue,” not “no shapes are blue.”
Common mix-up
Changing one word is not enough unless the new statement is true in exactly the cases where the original is false.
Exact meaning
For a statement p, its negation—written ¬p or read “not p”—is true exactly when p is false and false exactly when p is true.