1.

If A = \([(x,y):y = \frac{1}x,0≠ x∊R] \) and B [(x,y):y = - x,x ∊ R], then write A⋂B.

Answer»

Here,

A = {\((x,y):y = \frac{1}x,0≠ x∊R\)}and 

B = {(x,y):y = - x, xϵR 

A⋂B = {\((x,y):y = \frac{1}x,0≠ x∊R\)} and {(x,y):y = - x,xϵR}

= {\((x,y):-x = \frac{1}x, x∊R\)}

= {(x, y):-x2 =1,x ϵ R} 

= {(x, y):x2 =-1,x ϵ R} 

= ϕ (∵ there is no such that x2 = - 1)


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