Week 3: Mathematical Language and Symbols

It refers to a statement that is both universal and conditional which contains some variation of the words ‘‘for all’’ and conditional statements contain versions of the words ‘‘if-then’’

Universal Conditional Statement

It refers to a statement that is universal because its initial part says that a certain property is true for all objects of a given sort, and it is existential because its second part assets the presence of something.

Universal Existential Statement

It refers to a statement such that the first part assures that a certain object exists and is universal since the second part says that the question fulfills a specific property for everything of a specific kind.

Existential Universal Statement

It refers to denoting a set by enumerating all of its elements between braces

Set - Roster Notation

It refers to a set S and P(x) be a property that elements of S may or may not satisfy.We may define a new set to be the set of all element x in S such that P(x) is true.

Set - Builder Notation

This set is denoted as follows.

Set - Builder Notation

It refers to any two sets denoted by A and B such that every element of A is also an element of B, then A is called subset of B.

Subset

This language of set is written as (image) symbolically.

Subset

It refers to a given elements a nand b, the (a,b) denotes the ordered pair consisting of a and b, noting that a is the first element of the pair, and b is the second element.

Ordered Pair

Any two ordered pairs (a,b) and (c,d) are said to be _____ if and only if a = c and b = d.

equal

It refers to given sets A and B denoted by A x B read as ‘‘A cross B’’ where the set of ordered pairs (a,b) where a is in A and b is in B.

Cartesian Product