1967 AHSME Problems/Problem 38

Problem

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:

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

Solution

$\fbox{E}$

1967 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 37	Followed by Problem 39
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1967 AHSME Problems/Problem 38

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