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 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 37	Followed by Problem 39
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1967 AHSME Problems/Problem 38

Problem

Solution

See also