{X|X E N and x greater than or equal to 4}

This is a set theory problem:
| = means such that is

E = is a symbol used to replace the words "is an element of"

N= represents all natural numbers

answer choices are:
a) {5,6,7,...,100}
b) {5,6,7,...}
c) {4,5,6}
d) {4,5,6,...}

please, help!
thank you

the set is all integers greater than or equal to 4.

Looks like (d)

BTW,

| means "such that" -- lose the "is"

Well, well, well, it seems like we've got ourselves a set theory problem! Let's break it down, shall we?

We have the set X, defined as X | X E N and x ≥ 4. Now, what does that mean? It means that X is the set of all natural numbers greater than or equal to 4.

Now, let's take a look at our answer choices:

a) {5, 6, 7, ..., 100}: Whoa, who invited 100 to the party? That's definitely not part of our set X. So, this one is out.

b) {5, 6, 7, ...}: Ah, another never-ending party! But does it include all the natural numbers greater than or equal to 4? You bet it does! This is looking like a strong contender.

c) {4, 5, 6}: Aha, the culprits themselves! These are the only members of X that we know for sure. However, our dear friend X | X E N and x ≥ 4 tells us that there are more natural numbers involved. So, this one isn't quite right.

d) {4, 5, 6, ...}: Ah, there it is, the infamous "..."! This means that the party of natural numbers greater than or equal to 4 goes on and on. So, this set is a winner!

To sum it up, the set X | X E N and x ≥ 4 is represented by answer choice d) {4, 5, 6, ...}. Congratulations, you cracked the code!

To determine the set {X|X E N and X ≥ 4}, we need to consider the elements that meet two conditions:

1. X is an element of N (natural numbers)
2. X is greater than or equal to 4.

Checking the answer choices:

a) {5,6,7,...,100} - This set includes numbers from 5 to 100, but it does not include numbers less than 5.

b) {5,6,7,...} - This set includes numbers starting from 5 and continuing indefinitely. It does not have a lower bound of 4.

c) {4,5,6} - This set includes only three numbers: 4, 5, and 6. It does not include other natural numbers.

d) {4,5,6,...} - This set includes numbers starting from 4 and continuing indefinitely, which satisfies both conditions. Therefore, the correct answer is (d) {4,5,6,...}.

To determine the correct answer, we need to analyze the given set notation: {X | X E N and x ≥ 4}.

In this notation, "X" represents an element of the set, "E" indicates that the element is a member of, and "N" represents the set of natural numbers (positive integers). The condition "x ≥ 4" means that the element must be greater than or equal to 4.

Now, let's examine the answer choices:

a) {5,6,7,...,100}
b) {5,6,7,...}
c) {4,5,6}
d) {4,5,6,...}

a) {5,6,7,...,100}: This set includes numbers from 5 to 100. However, it doesn't include all natural numbers greater than or equal to 4, as it starts from 5.

b) {5,6,7,...}: Similar to option A, this set also starts at 5, excluding 4 which satisfies the given condition.

c) {4,5,6}: This set includes numbers 4, 5, and 6. However, it doesn't cover all the natural numbers greater than or equal to 4.

d) {4,5,6,...}: This set represents all the natural numbers greater than or equal to 4. It satisfies the given condition by including the number 4 and continuing indefinitely.

Therefore, the correct answer is option d) {4,5,6,...}, as it includes all natural numbers greater than or equal to 4.