Math Logic terms

Statement:

A statement is any sentence which is True or False, but not both.

Negation:

Changes the truth value by inserting or removing the word “____not______” ~

Rule: about negations truth value

The negation of a statement has the opposite truth value.

Conjunction (∧)

(∧) is a compound statement formed by combining two simple
statements using the word AND.

Rule: To make a conjunction true

BOTH statements need to be true

Disjunction (∨)

(∨) is a compound statement formed by combining two simple
statements using the word OR.

Rule: To make a disjunction true

true EITHER statement MUST be true or both can be true

Conditional ( →):

A compound statement formed by using the words IF... THEN to combine two simple sentences.

The Inverse

of a conditional statement is formed by negating the hypothesis and the conclusion.

Converse

of a conditional statement is formed by switching the position of the hypothesis and the conclusion.

The Contrapositive

of a conditional statement is formed by switching the hypothesis and the conclusion then
negating both

Biconditional (↔)

(↔) is a conjunction of a conditional and its converse. (... if and only if...)

Rule about Biconditionals

Only true when both statements have the same truth value

law of Disjunctinve Inference

Disjunction is true, One of the dijuncts is false, so the other is true

Law of Detachment

Need a conditional, Hypothesis is true so you can conclude the conclusion is also true