1967 AHSME Problem 38

Given a set S consisting of two undefined elements "pib" and "maa", and the four postulates: P_1: Every pib is a collection of maas, P_2: Any two distinct pibs have one and only one maa in common, P_3: Every maa belongs to two and only two pibs, P_4: There are exactly four pibs. Consider the three theorems: T_1: There are exactly six maas, T_2: There are exactly three maas in each pib, T_3: For each maa there is exactly one other maa not in the same pid with it. The theorems which are deducible from the postulates are:

\begin{array}{l} \textbf{(A)}\ T_3 \; \text{only}\qquad \textbf{(B)}\ T_2 \; \text{and} \; T_3 \; \text{only} \qquad \textbf{(C)}\ T_1 \; \text{and} \; T_2 \; \text{only}\\ \textbf{(D)}\ T_1 \; \text{and} \; T_3 \; \text{only}\qquad \textbf{(E)}\ \text{all} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.