True or False??

Algebra Level pending

Is there a set X X in which this is true?

( a + b ) 2 = a 2 + b 2 , ∀ ( a , b ) ∈ X × X (a + b)^2 = a^2 + b^2, \forall (a,b) \in X\times X

True False

Icaro Buscarini by Icaro Buscarini , 26, Brazil

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2 solutions

Icaro Buscarini
Sep 6, 2018

Solution: True

Take the following set : X = Z 2 = Z / 2 Z = { 0 ‾ , 1 ‾ } , X = \mathbb{Z}_2 = \mathbb{Z}/2\mathbb{Z} = \{\overline{0}, \overline{1}\}, such that, a ‾ = { x ; x ≡ a ( m o d 2 ) } , a ∈ { 0 , 1 } \overline{a} = \{ x ; x \equiv a (mod\hspace{1mm} 2) \}, a \in \{0, 1\} .

The equation is always true

2 Helpful 0 Interesting 0 Brilliant 0 Confused

An easy solution is the set ∅ \emptyset or the set { 0 } \{0\} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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