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If the operation (*) is defined for all integers a and b

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If the operation (*) is defined for all integers a and b by a (*) b = a + b - ab
I. a (*) b = b (*) a
II. a (*) 0 = a
III. (a*b)*c = a*(b*c)
Official Answer

1 Best Answer

Meenakshi Jain
1
Best answer
Statement I) a*b = b*a => a + b - ab = b + a - b Hence this is true.
Statement II) a*0 = a
Solve LHS
=> a + 0 - a.0 = a
Hence this is true
Statement III) (a*b)*c = a*(b*c)
Simplify LHS
=> ( a + b - ab) * c
=> a + b - ab + c - (a + b - ab)c
=> a + b - ab + c - ac - bc + abc
=> a + b + c - ab - ac - bc + abc
Simplify RHS
=> a * ( b + c - bc)
=> a + b + c - bc - a(b+c -bc)
=> a + b + c - bc - ab -ac + abc
=> a + b + c - ab - ac - bc + abc
LHS = RHS
Hence This statement is true.
Answer is E
answered Feb 15, 2015 by Senior Associate (449 points)
selected Feb 20, 2015 by
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