1. What is a set?

A set is simply a group of things listed or described. We usually show a set by putting the items inside curly braces like this: { }. These items can be anything, numbers, letters, words, or even everyday things like animals or types of food. An easy way to think about a set is to imagine it like a basket holding certain items that all belong together for a reason, and we know exactly what those items are.

2. Is it correct to say that a set is a collection of numbers or letters? Why yes or why not?Sets can include many different kinds of things besides just numbers or letters. For example, a set can contain words like colors or days of the week, such as {red, blue, green} or {Monday, Wednesday, Friday}. Sets can also have objects like animals or fruits, for example, {cat, dog, bird} or {apple, banana, grape}. In addition, sets can include ideas or feelings like {happiness, kindness, courage}, or symbols such as {+, -, =}. This shows that sets are flexible and can contain almost anything if the items are clearly defined and distinct.

3. What is an infinite set? Provide a minimum of two examples.

An infinite set is a set that goes on forever. For example,

{5. 10, 15, 20, 25, ...} is a set of positive numbers that are all multiples of 5. This set lasts forever because one can keep adding 5 to get the following number, so it has no end.

Another example is {-1, -2, -3, -4, ...}, which keeps going with negative numbers

4. What is the difference between equality and equivalence of sets? Support with a minimum of two examples.

The difference between equality and equivalence of sets is based on what the sets contain. Two sets are equal if they have the same elements, even if the order is different. For example,

Set A = {red, blue, green} and Set B = {green, blue, red} are equal because they contain the same items. The order does not matter in sets only the content does. On the other hand, two sets are equivalent if they have the same number of elements, even if the elements are different. For example,

Set P = {cat, dog, bird} and Set Q = {pen, paper, ruler} are equivalent because both have three elements, but are not equal since the actual items are different. Another example is

Set X = {apple, banana, orange} and Set Y = {circle, square, triangle}. These sets are also equivalent because each has three items, even though the items are not the same.

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