Set Theory - Buaft.com

Term Monoid in set theory

Term Monoid in set theory; A semi group is Monoid If it has identity element with respect to binary operation ∗ .Term Monoid in set theory image. A non empty …

properties of binary operation

properties of binary operation:Suppose that S be a non empty set And ∗ (read star) be a binary operation on set S ( means set S is closed with rest …

Define binary operation

An operation which is performed on two number and resultant values is another number of the same system is called binary operation. For Example 3 + 4 = 7 . …

Multiplicative inverse of real number

Multiplicative inverse of real number: The element ” 1 / a ” is called Multiplicative inverse of real number ” a ” Symbolically: ∀ a ∈ R ( a ≠ …

Reversal law of inverse

Reversal law of inverse statement: In a group G, ∀ ( for all) a , b ∈ G ⇒ ( this implies that ) (ab)⁻ ¹ = a⁻¹ b⁻¹ Proof: …

difference of two set

Difference of two set definition”The set of all element of A which does not belong to B”. The difference of two set A and B is denoted by mathematical symbol …

power set of empty set

power set of empty set,, power set of empty set is a singleton set. Let B = { } OR B = φ , then B has only one possible …

singleton set has proper subset

Every singleton set has no proper subset. For example {6} has one and only one subset {6}which is improper subset. Null set or empty set { } has no proper …

Set builder notation Example

Set builder notation Example: Set builder notation Example Descriptive form of set Tabular form of set Notation { x/x ∈ N ∧ …

Order of a set

Order of a set : There is no restriction on the number of members of a set . A set may have 0,1,2,3,4 or any number of elements. sets with …