Mathematical Statement

Universal Statement is a #202204281244 which states that certain properties are true for all elements in a set. It usually uses universal quantifier \(\forall\) which express for all, for every, for arbitrary, for any, for each and given any.

Some 202204281244 can express both property of #202204281245 and #202205062055 which make it a #202205061208, named Universal Conditional Statement.

Truth Table is a table that shows the truth value (true or false) of a #202204281244. It takes \(2^n\) steps to display all truth values, where \(n\) is the number of variables involved.

Proof by Division into Cases is a valid form of #202205062050. As the name suggests, the proof can be done if we exhausted all possible cases and all of them come up with the same 202204281244. This will be shown below:

In 202204281244#, however, Predicate (sometime called propositional function or open sentence) is a sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables. Let \(P\) be is a student at MMU and \(Q\) be is a student. Both \(P\) and \(Q\) are what we called the predicate symbols. If say the sentences are \(x\) is a student at MMU \(x\) is a student at \(y\) (\(x\) and \(y\) are predicate variables), then it is equivalent to express it in mathematical term \(P(x)\) and \(Q(x, y)\) respectively.

Necessary Condition is a condition where one 202204281244 solely depends on another statement. This could be expressed in 202205062055# as “if not \(r\), then not \(s\)”. “If \(s\) then \(r\)” means the same thing.

Two #202204281244 are logical equivalence when they share the same truth values# for all situation. For example: \(p\) and \(\sim (\sim p)\) are logical equivalence. The following is their truth table:

If a 202204281244 consists of both the property of 202204281254# and #202204281245, which is itself a kind of #202205061208, then it is an Existential Universal Statement

Existential Statement is a #202204281244 which states there is at least one thing for which the property is true, given that it could be either true or false. It usually uses existential quantifier \(\exists\) which express there is a, there exists, we can find a, there is at least one, for some and for at least one.

Conditional Statement is a #202204281244 which states that if one thing is true, then some other thing should be also true. It usually uses the phrase “if … then”.

Compound statement is a #202204281244 that consists of at least one primitive logical operator#. It expresses the relationship between different statements or the statement itself. For example: “is not \(p\)”, “\(p\) and \(q\)”, “\(p\) or \(q\) or both” and “\(p\) or \(q\) but not both”.

An argument is composed a sequence of multiple 202204281244#. The last sequence of it is the conclusion of the argument. All previous statements are called premises, assumptions or hypotheses. For an argument to be valid, both conclusion and premises must be valid in form and #logically sound.