An yield curve would be meaningless if it combines, for example, the yield on a AAA bond with the yield on a bond near default on the same curve. Therefore statement I is incorrect as any typical yield curve generally refers to similar instruments, and similarity includes similarity of issuer type and credit risk profiles.

Statement II accurately describes an yield curve, and statement IV explains what the term structure is.

Statement III is incorrect as the liquidity preference theory offers an explanation for an upward sloping yield curve and not a downward sloping one.