State which of the following sets are finite and which are infinite:
i) A={x: x in Z` and `x^2-5 x+6=0'}
ii) 'B={x: x in Z' and 'x^2' is even}
iii) 'C={x: x in Z.' and 'x^2=36'}
iv) 'D={x .: x in Z' and 'xgt-10}

Explanation

i) .A={x: x in Z.. and ..x^2-5 x+6=0=2,3}.

So, A is a finite set
ii) .B={x: X in Z.. and .x^2.} is even .-6,-4,-2,0,2,4,6 .... . ..
Clearly, .B. is an infinite set.
iii) .C:=x: x in Z.. and ..x^2=36=6,-6.
Cléarly, .C. is a finite set.
iv) .D=x: x in Z. and .xgt-10=-9,-8,-7, ldots ldots.
Clearly, Dis an infinite set.