Question

1. Decide whether each statement is true or false. Prove your answer (i.e. prove that it is true or prove that it is false.)

(a) There exists a nonzero integer α such that α · β is an integer for every rational number β.

(b) For every rational number β, there exists a nonzero integer α such that α · β is an integer.

Answer #1

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer
(whether “true “ or “false”).
If the cost of steel increases, then the supply of cars will
shift and this shift would cause a shortage of cars to open up at
the old equilibrium price (i.e., the price before the supply
shifted).

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For highly skewed data the sample median is a more sensible
measure of centre than the sample mean.
a) True
b) False
Q2. Read the statement below and decide whether it is
True or False.
Only properly designed and well executed experiments can
reliably establish causation.
a) True
b) False
Q3. Read the statement below and decide whether it is
True or False.
If the tail proportion...

Read the statement below carefully, and decide whether it is
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"false").
If two sets of data are inversely related, they will appear on a
graph as an upward-sloping line

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer (whether “true “ or
“false”).
A rightward shift in the money supply curve is likely to produce
a rightward shift in the money demand curve.

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer (whether “true “ or
“false”).
The net-export effect suggests that if an economy’s price level
decreases, then the economy’s net exports will decrease.

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer
(whether “true “ or “false”).
A straight line or curve can shift when a factor not included on
the vertical axis or horizontal axis changes.

Determine if each of the following statements is true or false.
If a statement is true, then write a formal proof of that
statement, and if it is false, then provide a counterexample that
shows its false.
1) For each integer a there exists an integer
n such that a divides (8n +7) and
a divides (4n+1), then a divides 5.
2)For each integer n if n is odd, then 8
divides (n4+4n2+11).

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer (whether “true “ or
“false”).
Along the Keynesian range of the aggregate supply curve, higher
aggregate demand fails to stimulate output and only causes
inflation.

1. For each statement that is true, give a proof and for each
false statement, give a counterexample
(a) For all natural numbers n, n2
+n + 17 is prime.
(b) p Þ q and ~ p Þ ~ q are NOT logically
equivalent.
(c) For every real number x
³ 1, x2£
x3.
(d) No rational number x satisfies
x^4+ 1/x
-(x+1)^(1/2)=0.
(e) There do not exist irrational numbers
x and y such that...

Read the statement below carefully, and decide whether it is
true or false. And then EXPLAIN your answer (whether “true “ or
“false”).
If the total production of final output in a nation is rising
and the general price level is also rising, then the nation’s real
GDP will be rising faster than its nominal GDP.

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