Question 38
Given a set $S$ consisting of two undefined elements “pib” and “maa,” and the four postulates:
$\mathrm{P}_1:$ Every pib is a collection of maas.
$\mathrm{P}_2:$ Any two distinct pibs have one and only one maa in common.
$\mathrm{P}_3:$ Every maa belongs to two and only two pibs.
$\mathrm{P}_4:$ There are exactly four pibs.
Consider the three theorems:
$\mathrm{T}_1:$ There are exactly six maas.
$\mathrm{T}_2:$ There are exactly three maas in each pib.
$\mathrm{T}_3:$ For each maa there is exactly one other maa not in the same pib with it.
The theorems which are deducible from the postulates are:
$\mathrm{P}_1:$ Every pib is a collection of maas.
$\mathrm{P}_2:$ Any two distinct pibs have one and only one maa in common.
$\mathrm{P}_3:$ Every maa belongs to two and only two pibs.
$\mathrm{P}_4:$ There are exactly four pibs.
Consider the three theorems:
$\mathrm{T}_1:$ There are exactly six maas.
$\mathrm{T}_2:$ There are exactly three maas in each pib.
$\mathrm{T}_3:$ For each maa there is exactly one other maa not in the same pib with it.
The theorems which are deducible from the postulates are: