
[ended]Mathematics Tutoring Session #7 (Binary Operation[Wed. 24rd Feb 2016, 4:00  5:00pm])
Global Update
Emmanuel Iwara(Tutor)
24022016 14:40:00 +0000Good day all,
This session has ended for today
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.

Omotayo Olalekan
When you guys are giving us questions to solve try and post one or two examples with you explanation. I'm not clear with what you wrote above seeing an example of yours would make me understand better.
0 24022016 14:54:00 +0000

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