radio modulation methods, carrier versus no carrier
>carrier is used so that antenna size can be reduced
No. Modulation methods that use carriers such as AM or FM do not require smaller antennas than modulation systems such as SSB when used at the same frequency.
>power can be transmitted to greater distances
No, the energy from a transmitter at a paticular frequency is attenuated the same amount with distance. The signal to noise ratio required at the receiver to give a usable signal does vary between modulation modes.
AM and FM recievers can be made more cheaply than recivers for other modes.