Download Sets and Properties of Equality

1.1-B
Sets
 Set – a collection of objects. Ex {a, e, i , o , u}
 Elements (members) – the individual objects in a set
 Null Set – a set that consists of no elements Ex. Ø
Sets
 Set Builder Notation – combines the use of braces
and the concept of a variable to define the elements of
a set. Ex {x|x is a vowel} is read “the set of all x such
that x is a vowel”. The vertical line inside the braces
represents the phrase “such that”. This describes the
set {a, e, i , o , u}.
 Equality – a statement in which two symbols or
groups of symbols are names for the same number. Ex
6 + 1 = 7; Ex 12/4 = 3
Properties of Equality
 Reflexive Property – For any real number “n”, n = n
Ex. 7 = 7; x = x; a + b = a + b
 Symmetric Property – For any real numbers “a” and
“b”, if a = b, then b = a Ex If 7 + 2 = 9, then 9 = 7 + 2;
Ex If x + 2 = 5, then 5 = x + 2
Properties of Equality
 Transitive Property – For any real numbers “a”, “b”,
and “c”, IF a = b AND b = c, THEN a = c
Ex. IF 3 + 4 = 7 AND 7 = 5 + 2 THEN 3 + 4 = 5 + 2
Ex. If x + 4 = y AND y = 9 THEN x + 4 = 9
 Substitution Property – for any real numbers “a” and
“b”: If a = b, then “a” may be replaced with “b” or vice
versa in any statement without changing its meaning
or value. Ex. IF x + y = 3, AND x = 2, THEN 2 + y = 3