U B
II
The accompanying Venn diagram shows the number of elements in region V. Use
the given cardinalities to determine the number of elements in each of the other
seven regions.
n(U) = 44, n(A) = 20, n(B) = 20,
n(C) = 28, n(ACB) = 8,
n(AnC) = 11, n(BNC) = 15
I
III
IV
V
6
VI
There are
VII
VIII
There are
There are
There are
There are
There are
There are
elements in region I.
elements in region II.
elements in region III.
elements in region IV.
elements in region VI.
elements in region VII.
elements in region VIII.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?