Generate Quiz 69F67B8D9EE3F

C (singleton) is the response.

a) A set with countable elements is called a finite set.

b) Empty set has no element.

c) A singleton contains a single element.

d) There were an infinite number of elements in the infinite set.

The set is a singleton since there is only one even prime natural number, which is 2.

(d) all of these is the right choice.

Any number that can be represented as a fraction with an integer denominator (q) and numerator (p) and a non-zero denominator (q ≠ 0) is considered a rational number. Zero satisfies the criteria for being a rational number since it can be written as 0/1, 0/2, and so forth.
A whole number, including zero, that can be either positive, negative, or zero is called an integer. This includes zero.

An integer that is precisely divisible by two is called an even number. Zero is an even number since it is equal to 0 divided by 2.

The modulus or absolute value of the complex number z is denoted by the notation [z]. Any number’s non-negative distance from zero is its absolute value.

The absolute value of a complex number in rectangular form, z = x + yi, can be accurately calculated using the given formula, [z] = √(x² + y²). This is the reason:

On the complex plane, the horizontal (real) and vertical (imaginary) components of the complex number z are represented by the real numbers x and y.

When x and y are squared, their squares will always be positive, even if they are negative.

The real and imaginary contributions to the total distance from zero are combined when the squares (x² + y²) are added.

The final magnitude, which is always non-negative, is obtained by taking the square root (√).

Any number that can be represented as a fraction with an integer (whole number) in the numerator and a non-zero denominator is considered rational. Any number that cannot be represented in this manner as a fraction is considered irrational.

The decimal 0.1428571428571… repeats. A fraction can always be used to express this type of decimal representation.

Let us take the repeating decimal 0.5555, for instance.

We can allow this decimal to be equal to x. After that, we obtain the following by multiplying both sides of the equation by 10:

10x = 5.5555…

The result of subtracting the two equations is:

9 times is 5.

x = 5/9

Thus, the rational number 5/9 can be represented as 0.5555…

By using the same reasoning, we can determine that 0.1428571428571… is a rational number by expressing it as a fraction.

When a and b are real numbers, the complex number z* = a – bi is the conjugate of the complex number z = a + bi. Stated differently, the sign of the imaginary unit (i) is changed to form the conjugate. Thus, (A) a-ib is the right choice.