
[ended]Mathematics Tutoring Session #7 Binary Operation on Wed. 24th Feb 2016 @ 4:00  5:00pm
Mathematics
Emmanuel Iwara(Tutor)
24022016 12:01:00 +0000Good day all,
The concept of Binary Operation is the most fundamental in mathematics often tested on JAMB and other exams. so lets take a quick look into this topics.
Binary Operation  Any rule of combination of any two elements of a given non empty set.
Closure Property of Binary Operation  A nonempty set P is said to be closed under a binary operation * if for all a, b∈P, a*b∈P
Commutative Property  Given a non empty set P which is closed under a binary operation *, if for all a,b∈P
a * b = b * a, then the binary operation * is said to be commutative.
Associative Property  If a, b, C∈P and P is closed under a binary operation *, then (a * b)* c = a * (b * c)
Distributive Property  Given that a nonempty set P is closed under the operation * and ⊕; if for all a, b, c∈P
then a * (b⊕c) = (a * b)⊕(a * c) (Left Distributive over ⊕)
(b⊕c)* a = (b * a)⊕(c * a) (Right Distributive over ⊕)
Identity or Neutral Element  Given a non empty set which is closed under a binary operation *, if there exists an element e∈P such that x * e = e * x = x,then e is called Identity element.
Inverse Property  Given a non empty set P which is closed under a binary operation*, if for x∈P, there exist x'∈P such that x * x' = x' * x = e
where e is the Identity element in P under the operation *, then x' is called the inverse of x in P
Please feel free to ask questions where you do not understand.
Now lets try solving the questions below;
The correct solutons will be posted after the section is over stay close.
1.The binary operation (*) is defined by x * y = xy  y  x for all real values of x and y.
If (x * 3) = (2 * x), find x. (Jamb question number (22), 1998).
2. If a * b = √ab, evaluate 2 * (12 * 27). (Jamb question number (22), 1995).
3 .A binary operation * is defined by a * b = ab + a + b for any real number a and b. If the identity element is zero. Find the inverse of 2 under this operation. (Jamb question number (19), 1999).
4. If x * y = x + y  xy, find x, when (x * 2) + (x * 3) = 63. (Jamb question number (22), 1997).
**Note that this session begins from 3:00  4:00pm. Before the session begins, you can put down your questions on paper and then ask them when the session officially begins by 3:00pm.

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