If A = {(x, y) : y = ex , xϵR} and B = {(x, y) : y = e−x , xR}, the – InterviewSolution

InterviewSolution

1.

If A = {(x, y) : y = ex , xϵR} and B = {(x, y) : y = e−x , xR}, then write A⋂B.

Answer»

Here,

A = {(x,y):y = e^x,xϵR} and

B = {(x,y)y = e^-x,xϵR}

A⋂B = {(x,y):y = e^x ,xϵR} and {(x,y):y=e^-x ,xϵR}

= {(x,y):y = e^x and y = e^-x xϵR}

= {(x,y): e^x = e^-x xϵR}

= {(x,y):e^x = \(\frac{1}{e^x}\),xϵR}

= {(x,y):e^2x = 1,xϵR}

= {(0,1)} (∵e⁰ = 1 )

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