1.

whichofthefollowingsets in notfinite ? {(x,y):x^(2)+y^(2)le1lex+y,x,yin R}

Answer»

`{(X,y):x^(2)+y^(2)le1le x+y, x,yin R]`
`{(x,y):x^(2)=+ y^(2)le1le x+y, x,y in Z}`
`{(x,y):x^(2)le yle |x|,x,y in Z}`
`{(x,y):x^(2)le yle|x|,x,yin Z}`

Solution :the set `{(x,y):x^(2)+y^(2)le1lex+y,x,yin R}` CONSISTS of all pointin thefirstquadrantwhichlieinsidethecircle`x^(2)+y^(2)=1`andabovethe line`x+y=1`. So it is NOTA finite set
we have ,
`{(x,y):x^(2) +y^(2)=1,x=Z}={(0,1),(0,1),(-1,0),(0,-1)}`
whichis afiniteset .
hence, option(a)is correct .


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