answer:To show that the intersection of set A and set B is a subset of set A and a subset of set B, we first need to find the intersection of set A and set B. The intersection of two sets is the set of elements that are common to both sets. In this case, the intersection of set A and set B is: A ∩ B = {2, 4} Now, we need to show that this intersection is a subset of both set A and set B. A subset is a set whose elements are all members of another set. In other words, if all elements of set X are also elements of set Y, then set X is a subset of set Y. Let's check if the intersection A ∩ B is a subset of set A: A ∩ B = {2, 4} A = {1, 2, 3, 4, 5} Both elements 2 and 4 are members of set A. Therefore, A ∩ B is a subset of set A. Now, let's check if the intersection A ∩ B is a subset of set B: A ∩ B = {2, 4} B = {2, 4, 6, 8} Both elements 2 and 4 are members of set B. Therefore, A ∩ B is a subset of set B. In conclusion, the intersection of set A and set B, which is {2, 4}, is a subset of set A and a subset of set B.

answer:To prove that the intersection of set A and set B is a subset of set A and set B, we need to show that every element in the intersection of A and B is also an element of A and an element of B. Let's find the intersection of set A and set B: A ∩ B = {x | x ∈ A and x ∈ B} Comparing the elements of set A and set B, we can see that the elements 3, 4, and 5 are common to both sets. Therefore, the intersection of set A and set B is: A ∩ B = {3, 4, 5} Now, let's prove that A ∩ B is a subset of set A and set B. 1. A ∩ B ⊆ A: For every element x in A ∩ B, x must also be an element of A. Since A ∩ B = {3, 4, 5}, we can see that all elements in A ∩ B are also elements of A = {2, 3, 4, 5}. Therefore, A ∩ B is a subset of A. 2. A ∩ B ⊆ B: For every element x in A ∩ B, x must also be an element of B. Since A ∩ B = {3, 4, 5}, we can see that all elements in A ∩ B are also elements of B = {3, 4, 5, 6}. Therefore, A ∩ B is a subset of B. Since A ∩ B is a subset of both set A and set B, we have proven that the intersection of set A and set B is a subset of set A and set B.

answer:To find the intersection of sets A and B, we look for the elements that are common to both sets. In this case, the intersection of A and B is: A ∩ B = {3, 4} Now, we need to verify if this intersection is a subset of both A and B. A subset is a set whose elements are all members of another set. In other words, if all elements of set X are also elements of set Y, then set X is a subset of set Y. Checking if A ∩ B is a subset of A: All elements in A ∩ B = {3, 4} are also elements of A = {1, 2, 3, 4}. Therefore, A ∩ B is a subset of A. Checking if A ∩ B is a subset of B: All elements in A ∩ B = {3, 4} are also elements of B = {3, 4, 5, 6}. Therefore, A ∩ B is a subset of B. In conclusion, the intersection of A and B (A ∩ B) is a subset of both A and B.

answer:To prove that A ∩ B is a subset of both set A and set B, we need to show that every element in A ∩ B is also an element in A and in B. First, let's find the intersection of sets A and B: A ∩ B = {x | x ∈ A and x ∈ B} Comparing the elements of both sets, we can see that: A ∩ B = {4, 6, 8} Now, let's prove that A ∩ B is a subset of A: For every element x in A ∩ B, x must also be an element in A. We can see that all elements in A ∩ B (4, 6, and 8) are also elements in A: 4 ∈ A, 6 ∈ A, and 8 ∈ A Since every element in A ∩ B is also an element in A, we can conclude that A ∩ B is a subset of A. Now, let's prove that A ∩ B is a subset of B: For every element x in A ∩ B, x must also be an element in B. We can see that all elements in A ∩ B (4, 6, and 8) are also elements in B: 4 ∈ B, 6 ∈ B, and 8 ∈ B Since every element in A ∩ B is also an element in B, we can conclude that A ∩ B is a subset of B. Therefore, we have proven that A ∩ B is a subset of both set A and set B.