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Mathematics Tutoring Session #7 (Binary Operation[Wed. 24rd Feb 2016, 4:00 - 5:00pm])
Global Update
Emmanuel Iwara(Tutor)
24-02-2016 14:32:00 +0000BINARY OPERATION Good 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 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
Feel free to ask your questions, if you have any, i will try to answer them.
Can anyone 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 (22), 1998.
2.If a*b = √ab, evalute 2 * (12 * 27).Jamb question (22), 1995.
3.A binary operation * is defined by a * b = ab + a+b for any real number aand b. If the identity element is zero. Find the inverse 0f 2 under this operation.Jamb question (19), 1999.
4.If x * y = x+y -xy, find x, when (x * 2) + (x * 3) =63.Jamb question (22), 1997.
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Emmanuel Iwara(Tutor)
@Prosper Ojo i will, but read through for a better understanding
0 24-02-2016 15:03:00 +0000
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Emmanuel Iwara(Tutor)
@Funke Ayoola, stay close at the end of this section i will post the solutions.
0 24-02-2016 15:06:00 +0000
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Emmanuel Iwara(Tutor)
@Prosper .Binary operation is any rule of combination of any two elements of a given non-empty set. A binary operation is usually denoted by *. the most familiar examples of binary operations are those of addition, subtraction, multiplication and division of real numbers. i 'll continue stay close.
0 24-02-2016 15:14:00 +0000
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Emmanuel Iwara(Tutor)
@Prosper. Binary operation is made up of properties (a) closure property which says a non empty set p is said to be closed under a binary operation* if a,b element of p. i'll continue are you there.
0 24-02-2016 15:19:00 +0000
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Emmanuel Iwara(Tutor)
@Funke Ayoola .Solution to question 1, since x*y = xy -y-x, then (x*3) will be 3x -3 -x,that is x=x, y=3 into the given problem, similarly (2*x) = 2x -x-2 = x-2 following the same approach.but (2*x) = (x*3) that gives us 2x-3 = x-2, simplifying for x gives (x) the value of 1.
0 24-02-2016 15:29:00 +0000
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