Could anyone help me understanding this question ?
List the members and find the cardinality of the following sets :
$$A=\{x\mid x \text{ is a real number such that } x^4=4\}$$
$$B=\{x\mid x = 2n – 5, x \text{ and }n \text{ are natural numbers}\}$$
$$C=\{x\mid x \text{ is a prime number less than } 100\}$$
$$D=\{x\mid x \text{ is the square of an integer and } x<200\}$$
For $C$ and $D$, I was able to solve it. For $A$, I'm not sure but I think it's equal to the empty set (there is no number that fit the formula).
I found an answer that say $B=\{1, 3, 5, 7, \dots\}$ but I didn't get it!!
Could you help me understand how to solve $B$ please!!
Best Answer
Welcome.
Cardinality means just the size of the set. How many numbers are there in the set of natural numbers $\mathbb{N}$?
For $A$, just power both sides by $\frac{1}{4}$, is this a real number? and since $x$ is even powered, you have both positive and negative solutions.
For $B$, first you know that $n$ is a natural number, meaning $n = 1, 2, 3, 4, 5, \dots$. Just plug in $n$ into the equation of $x$, what $x$ do you get? From this $x$, which of them are also natural numbers?
Hope it helps,