We define the binary operator, ∘ such that a ∘ a = a + 2 , a ∘ b = { a + 1 , if a > b b + 1 , if b > a .
Is this statement correct?
( x ∘ y = x + 1 ) OR ( x ∘ y = y + 1 ) = ( x ∘ y = x + 2 )
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Both sides satisfy the same condition. Given statement says both sides are not equal .
Therefore given statement is FALSE .
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Yes, I illustrated in the solution that both sides are equal. If it say "not equal", then the statement is FALSE .
Lets take left hand side:
L.H.S = (x∘y=x+1) OR (x∘y=y+1)
According to rules: x∘y = x+1 if x>y And x∘y = y+1 if y>x We can write,
L.H.S = x>y OR y>x
Either x is greater or y. Thus we can say x≠y
L.H.S = x≠y
Lets take right hand side:
R.H.S = (x∘y≠x+2)
According to first rules: x∘y=x+2=y+2 if x=y (In other words x∘x=x+2)
We can also write this as: x∘y≠x+2≠y+2 if x≠y
R.H.S = x≠y
Left hand side = Right hand side
((x∘y=x+1) OR (x∘y=y+1))=(x∘y≠x+2) Is True
But ((x∘y=x+1) OR (x∘y=y+1))≠(x∘y≠x+2) Is False
Useful Information:
The operator ∘ is called Zeration also known as Hyper0,Increment and Successor.
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a ∘ b = ⎩ ⎪ ⎨ ⎪ ⎧ b + 1 , if a < b a + 2 , if a = b a + 1 , if a > b
If on the left-handed side, the result is either x + 1 or y + 1 , then x = y . If x = y , then the result on the right-handed side shall also be either x + 1 or y + 1 , and not x + 2 . Given both sides satisfy the same condition, the equation shall be TRUE (it shall be equal sign, not = . The question said it is = , hence the answer is FALSE )