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Flashcards: Sets 19 Flashcards 
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Card: 1 / 19 
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What is a set in mathematics? |
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Card: 2 / 19
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A set is a collection of distinct objects, considered as an object in its own right. Sets are usually denoted by curly braces. For example, the set of even numbers can be written as {2, 4, 6, 8, ...}. |
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Card: 3 / 19
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What is the union of two sets? |
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Card: 4 / 19
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The union of two sets A and B, denoted as A ∪ B, is the set of elements that are in A, in B, or in both. For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}. |
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Card: 5 / 19
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What does it mean for a set to be a subset? |
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Card: 6 / 19
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A set A is a subset of a set B, denoted A ⊆ B, if every element of A is also an element of B. For example, if A = {1, 2} and B = {1, 2, 3}, then A is a subset of B. |
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Card: 7 / 19
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How do you find the intersection of two sets? |
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Card: 8 / 19
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The intersection of two sets A and B, denoted as A ∩ B, is the set of elements that are common to both A and B. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}. |
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Card: 9 / 19
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What is the largest planet in our Solar System?
Solution:
Jupiter is the largest planet in our Solar System, known for its massive size and distinctive bands of clouds. It has a diameter of about 86,881 miles (139,822 kilometers), making it more than 11 times wider than Earth. Jupiter is a gas giant, primarily composed of hydrogen and helium, and it also has a very strong magnetic field and dozens of moons, including the largest moon, Ganymede.
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Card: 10 / 19
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Given the sets A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ B and A ∩ B? |
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Card: 11 / 19
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The union A ∪ B = {1, 2, 3, 4, 5} includes all unique elements from both sets. The intersection A ∩ B = {3} includes only the elements that are in both sets. |
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Card: 12 / 19
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If A = {x | x is an even integer} and B = {x | x is a positive integer}, what is A ∩ B? |
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Card: 13 / 19
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A ∩ B = {2, 4, 6, 8, ...} includes all positive even integers. This set consists of elements common to both sets. |
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Card: 14 / 19
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What is the formula to find the number of subsets of a set with n elements? |
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Card: 15 / 19
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The number of subsets of a set with n elements is given by 2ⁿ. For example, if n = 3, the set has 2³ = 8 subsets. |
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Card: 16 / 19
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How many elements are in the power set of A = {1, 2, 3}? |
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Card: 17 / 19
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The power set of A contains all possible subsets of A, including the empty set and A itself. Since A has 3 elements, the power set has 2³ = 8 elements. |
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Card: 18 / 19
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If A = {1, 2, 3} and B = {3, 4, 5}, what is the number of elements in A ∪ B? |
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Card: 19 / 19
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A ∪ B = {1, 2, 3, 4, 5} has 5 elements. Therefore, the number of elements in A ∪ B is 5. |
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 Completed! Keep practicing to master all of them. |
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