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24-02-2016 14:40:00 +0000
Good 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 non-empty 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 non-empty 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;
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).
24-02-2016 14:48:00 +0000
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.
24-02-2016 14:54:00 +0000
Yeah dat true
24-02-2016 14:58:00 +0000
24-02-2016 14:59:00 +0000
24-02-2016 15:02:00 +0000
plz I don't understand did question chindima
24-02-2016 15:03:00 +0000
24-02-2016 15:04:00 +0000
did u understand chidinma
24-02-2016 15:05:00 +0000
24-02-2016 15:10:00 +0000
we need an example in show working