how come there is no ike dollar in 1971 u.s. proof set?

Answer 1

It didn't please the Mint to creat "proof" dollar coins that year. That year a pricier 40% silver version was offered instead.

Answer 2

They didn't start to put them in until 1973. The 1971-S proofs were silver clad and available from the mint only by themselves in a plastic holder in a brown box. The 1972-S is the same. In 1973 they came out with the copper nickel S clad proofs as well a the silver clad. The copper-nickel clad were in the proof sets of that year, as well as following years. There are none dated 1975. Hope this clears things up. One never knows what the mint is up too.