Find the product.
1 answer:
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Answer:
a) False
b) False
Step-by-step explanation:
We are given the following information:
Z is a set of all integers, is a set of all positive integers and
is a set of all negative integers.
Q is a set of all rational numbers, is a set of all positive rational numbers and
is a set of all negative rational numbers.
N is a set of all natural numbers.
a) False
We will show this with the help of a counter example.
which is a rational number and not an integer.
b) False
We will show this with the help of a counter example.
which is a rational number and not a natural number.
Substituting <em>x</em> with <em>π</em>/2 - <em>x</em> gives the equivalent integral,
So if we let <em>J</em> denote the value of the integral, we have
Condensing the logarithms, we have
log(tan(<em>x</em>)) + log(cot(<em>x</em>)) = log(tan(<em>x</em>) cot(<em>x</em>)) = log(1) = 0
since cot(<em>x</em>) = 1/tan(<em>x</em>), which means
and so the original integral has a value of <em>J</em> = 0.