If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)
a. I
b. II
c. I & II
d. I & III
e. I, II & III
The answer of the above problem is e. I am looking for a short and smart way to solve this problem.
Cheers!
a # b = a + b – ab
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Ahmed MS wrote:If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)
- I. a # b (a + b - ab) and b # a = b + a - ab ----> TRUE
II. a # 0 = a + 0 - a*0 = a ----> TRUE
III. (a # b) # c = (a # b) + c - (a # b)c = (a + b - ab) + c - (a + b - ab)c = (a + b + c - ab -bc - ca + abc) = a + (b + c - bc) - a(b + c - bc) = a + (b # c) - a(b # c) = a # (b # c) ----> TRUE
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I) a#b = b#aAhmed MS wrote:If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)
a. I
b. II
c. I & II
d. I & III
e. I, II & III
The answer of the above problem is e. I am looking for a short and smart way to solve this problem.
Cheers!
a+b-ab = b+a-ba
II)a#0 = a
a+0-a*0= a-0 = a
III) (a # b) # c = a # (b # c)
a+b-ab+c- c(a+b-ab) = a +(b+c-bc) - a(b+c-bc)
a+b-ab+c - ac-bc+abc = a+b+c-bc - ab-ac+abc
-ab = - ab
or you can use numbers
a=1 b=2 c=3