Translation, Logical connectives, WFF, and 3 operations

Negation

¬ or ~

"Not" - negates the truth value of a statement. Example: "It is not raining" → ¬R.

Conjunction

∧

"And" - the compound statement is true only if both parts are true. Example: "It is raining and it is cold" → R ∧ C.

• if one is false then false

• both need to be true to be true

Disjunction

∨

"Or" - the compound statement is true if at least one of the parts is true.

Example: "It is raining or it is cold" → R ∨ C.

• True if At least one disjunct is 2) true.

• false if both are false

Implication

→

"If...then..." - the compound statement "P → Q" is false only if P is true and Q is false.

Biconditional

↔

"If and only if" - both statements must have the same truth value. Example: "It is raining if and only if the ground is wet" → R ↔ W.

A well-formed formula (WFF)

a grammatically correct symbolic expression."

A statement variable

a lowercase letter that serves as a placeholder for any statement—for example, p, q, r, s.

Conversion

- Swap subject/predicate

- Valid for E/I: "No A are B" ↔ "No B are A."

Invalid for A/O.

Obversion

Change quality + negate predicate.

Always valid: "All A are B" → "No A are non-B."

Contraposition

Swap and negate both terms.

Valid for A/O: "All A are B" ↔ "All non-B are non-A."