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Que: if : r>r is a function, scr,s is countable and tcr, tis uncountable set, then (a)f(s) is countable iffis oe-one (b) f{s) is countable if f is not one-one ©
Que: If : R>R is a function, SCR,S is countable and TCR, Tis uncountable set, then (a)f(S) is countable iffis oe-one (b) f{S) is countable if f is not one-one © fT) is countable if fis one-one (d) f(T) is countable if fis not one-one
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Shashi ranjan sinha Best Answer
S is countable implies f(S) is countable, doesn't matter f is one-one or not......but if T is uncountable, then f is one-one implies f(T) is uncountable and in case f is not one-one, then you cannot say with certainty anything. f(T) in that case may be countable or may be uncountable
so, options 1 and 2 are true