BINARY OPERATIONS

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	K	L	M
K	L	M	K
L	M	K	L
M	K	L	M

The identity element with respect to the multiplication shown in the table above is

(a)    O    (b)  M    (c)  L    (d)  K

Answer:          Option B

Reason:

a  e = a{That is an identity element under multiplication is that number e that when it multiply another number a, still gives a}

In the above table this occur where

                        K  M = K

                        L  M =L

                        M  M=M

 

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	P	q	r	s
p	r	p	r	p
q	p	q	r	s
r	r	r	r	r
s	q	s	r	q

The identity element with respect to the element shown in the table above is

(A)  p    (B)  q   (C)  r  (D)  s      

Answer: Option B

Reason

a  e = a{That is an identity element under multiplication is that number e that when it multiply another number a, still gives a}

In the above table this occur where

p  q = p

q  q = q

r  q = r

s  q =s

So we can see that q is an identity element under this operation.

 

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Answer:          Option B

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A binary operation  is defined on the set of all positive integers by a  b for all positive integers a,b, which of the following properties does not

A   Closure       B.       Associativity       C.      Identity        D.    Inverse

Answer:          Option D        

 

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mod 10	2	4	6	8
2	4	8	2	6
4	8	6	4	2
6	2	4	6	8
8	6	2	8	4

The multiplication table above has modulo 10 on the set S =(2,4,6,8). Find the inverse of 2

(UME 1994, Question 23)                                                                                                                               

1. 2
2. 4
3. 6
4. 8

 

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A binary operation * defined on the set of positive integer is such that  for all positive integer x and y, the binary operation is                                                                

(a)        Commutative and closed on the set of positive integers

(b)        Neither commutative nor closed on he set of positive integer

(c)        Commutative but not closed on the set of positive integers

(d)        Not commutative but closed on the set of positive integers

(UME 2008, Question 21 set U03, type A)

Answer: Option B

 

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A binary operation on the set of real number excluding –1  is such that for m, n ,

, find the identity element of the operation

(a) 1 (b) 0  (c)  – ½  (d) –1 (UME 2008, Question 21 set U03, type A)

 

Solution

The identity element is 0

Answer: Option B

 

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If  for any real number m and n. Find the value of

(a) – 6  (b)  –8    (c)  –10  (d)  –12

(UME 2008, Question 20 set U03)

 

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Answer: Option C

 

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A binary operation  defined on the set  of integers is such that  for all        integers m and n. Find the inverse of  –5 under this operation, if the identity element is 0               

Solution

Answer: Option A