Discrete Structures Terms

Proposition

A statement that is either true or false — not a question

NOT statement

Flips a statement to its opposite — true becomes false

AND statement

Both A and B have to be true — if even one side is false the whole statement is false

OR statement

At least one side has to be true — only false when both A and B are false

IF THEN statement

A has to happen first — only false when A happens but B does not follow — if A never happens the statement is true

IF AND ONLY IF statement

Both sides have to match — both true or both false means true — if one happens and the other doesn’t the statement is false

Predicate

A statement with a variable in it that becomes true or false only once you fill the variable in

Universal quantifier

Written as ∀ — means for all or for every — the claim has to hold for every single case with no exceptions

Existential quantifier

Written as ∃ — means there exists or there is at least one — only needs one example to be true

Converse

Flips an IF THEN statement — if A then B becomes if B then A — not necessarily the same meaning as the original

Inverse

Negates both sides of an IF THEN — if A then B becomes if NOT A then NOT B — not necessarily the same meaning as the original

Contrapositive

Flips and negates both sides of an IF THEN — if A then B becomes if NOT B then NOT A — always has the exact same meaning as the origina