IIT JAM
Gokul Asked a Question
October 11, 2020 4:53 pmpts 30 pts
  • IIT JAM
  • Mathematics (MA)

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-on...
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    Shashi ranjan sinha
    so, options 1 and 2 are true
  • Deepak singh
    since S is countable then f(S) is always countable either f is one one or not .. and f(T) may be uncountable . So option a and b are correct
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  • Piyush
    Option ABD are correct
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